It seems both aircraft were porpoising before going in. Is it possible the crews were trying to overcome excessive aerodynamic loads on the stabiliser which had gone towards the forward limit, after cutting electrical power to the stab trim motor and were now trying to wind manual trim during the unloading maneuver called roller coasting? See extract from a Boeing 737-200 PTM date 1982 and migrated from Tech Log
Extract from the Boeing 737-200 Pilot Training Manual February 1982 page 04.80.31. Edited for brevity
Runaway and Manual Stabiliser - Recovery from Severe Out-of-Trim
"In an extreme nose-up out-of-trim condition, requiring almost full forward control column, decelerate, extend the flaps and/or reduce thrust to a minimum practical setting consistent with flight conditions until elevator control is established. Do not decrease airspeed below the minimum maneuvering speed for the flap configuration. A bank of 30 degrees or more will relieve some force on the control column. This, combined with flap extension and reduced speed should permit easier manual trimming.

If other methods fail to relieve the elevator load and control column force, use the "roller coaster" technique. If nose-up trim is required, raise the nose well above the horizon with elevator control. Then slowly relax the control column pressure and manually trim nose-up. Allow the nose to drop below the horizon while trimming. Repeat this sequence until the airplane is trim.

I haven't seen it posted, apologies if it is a duplicate:

From BEA | Bureau d'Enquêtes & d'Analyses, via Twitter
It states that the FDR data have been downloaded and transferred to the Ethopian investigation team.
The CVR data have been downloaded and transferred the day before, on March 16th.

And the Ethiopian Transport Minister, Dagmawit Moges, held a press conference on Sunday, stating
"Clear similarities were noted between Ethiopian Airlines Flight 302 and Indonesian Lion Air Flight 610, which would be the subject of further study during the investigation,"
Details here:
https://www.bbc.com/news/world-africa-47605265

I understand that some data revealed by the CVR (or by both the CVR and FDR) confirmed the similarities between the 2 flights.

A video of the press conference can be found here
The language appears to be Amharic.

Cause of Ethiopian crash
 

I am not a pilot or aviation expert. My interest is because my late father was a research engineer at the Royal Aircraft Research Establishment in Farnborough, and we used to discuss air crashes and their causes. I continue to be interested. Sifting through the information to date, and the excellent journalism by the Seattle Times, this is my layman's take on the likely cause of Ethopian plane crash. Am I close?

Why the Boeing 737 Max 8 crashed in Ethiopia in March 2019

The Boeing 737 Max 8 has larger engines mounted further forward than on previous versions. This causes the possibility of a stall on take-off, as it can make the Angle of Attack (AOA) too steep. To compensate, Boeing introduced a "small" software fix (the MCAS) to automatically adjust this, pointing the plane nose down. It was considered so small a fix that it was not included in initial documentation for the updated jet or in information for pilot retraining.

Meanwhile the US FAA (Federal Aviation Administration), citing staff and budget shortages, had earlier delegated some aspects of safety assurance for the plane, back to Boeing, making it self regulating in some areas, including the MCAS fix. The FAA also seems to have been keen to help Boeing get the new plane certified and available for sale as it was facing stiff competition from the Airbus.

During testing it emerged that the AOA adjustment made by the MCAS software was insufficient and so this was increased by a factor of 4, however this was not updated in the safety documents (according to unnamed informants). In addition the MCAS software resets itself from scratch every time it is activated. All this means that if there is a faulty reading from one of the external AOAs, the MCAS will continuously reset the nose of the plane downwards, as if it was doing it for the first time each time.

In the safety documentation, an AOA sensor failure is classified as a serious hazard but not as catastrophic which would have caused a delay in certification. Some experts say that a single point of failure like this is catastrophic while others say an experienced pilot should be able to handle it.

This AOA sensor failure is what seems to have happened with the Lion air fatal crash of a Boeing 737 max 8 in Indonesia last October. At that time the pilots did not know about the MCAS fix. The existence of the MCAS came to light after this and its existence was then included in pilots retraining. The official report on the Lion Air disaster is not due out until later this year. Boeing has been working on a fix since then but says it was delayed by the public sector shut down in the US earlier this year and it is now due in May.

Initial indications are that a similar accident occurred with last week's fatal Boeing crash in Ethopia.

Boeing tumbled early Monday on heightened scrutiny by regulators and prosecutors over whether the approval process for the company’s 737 Max jetliner was flawed.

A person familiar with the matter on Sunday said that the U.S. Transportation Department’s Inspector General was examining the plane’s design certification before the second of two deadly crashes of the almost brand-new aircraft.

Separately, the Wall Street Journal reported that a grand jury in Washington, D.C., on March 11 issued a subpoena to at least one person involved in the development process of the Max. And a Seattle Times investigation found that U.S. regulators delegated much of the plane’s safety assessment to Boeing and that the company in turn delivered an analysis with crucial flaws.

737 Max Is Turning Into a Major Problem for Boeing | Time

You're mistaken, "climbing" (or, put more precisely) elevator/AOA control always controls speed. Of course, under the likely MCAS scenario discussed, they did not have AOA control and the airspeed was running away from them.

And thrust always controls vertical flight path, so if they reduced thrust they would have only hit the ground sooner. In a desperate fight for altitude, "piloting" would dictate maximum thrust.

But more speed when your stab trim is too nose down is your enemy. Reduction in speed would reduce the force to counter the nose down trim so 'piloting' would dictate reducing speed.

Fail operation versus fail passive.

Yes but reducing thrust on the 737 creates a large nose down moment (pitch/power couple) so as Vessbott stated they would have just hit the ground sooner.

My experience of this is unusual attitude recovery during manual reversing air tests. Reducing thrust, if you're already using everything you have to keep the nose up, WILL result in a further nose down moment and no reduction in speed. They'd have been better off sticking the speed brakes up.

And in fact Boeing DO publish this in the QRH.

In your proposed solution, had they reduced thrust what would have prevented them from diving into the ground at the high speed commanded by their low AOA?

I think here is a missunderstanding.
It's about channels not number of AP.

To my limited knowledge the 737 has no AP YAW CHANNEL, only roll and pitch.

Stand to be corrected.

Yes you're quite right. My bad.

Fail-operational autopilot is a customer option on the NG and MAX since 2003. Not many airlines have taken the option though...

You're right about the thrust pitch couple, but I'm not even talking about that yet, I'm only taking talking about the basic effect of excess thrust on flight path angle.

And to that end, I'm afraid spoilers won't help either, but they'll certainly be a lot less harmful than a thrust reduction with underslung engines.

Unless the pitching moment they add is nose up, which is an answer I don't know. But a nose up pitching moment is what we want, both for the instantaneous normal acceleration upward, and the energy-state perspective on reducing airspeed.
[/QUOTE]

It is runaway stab trim...
Maybe not all at once, but if it is not doing what you want, then it is out of control.

[/QUOTE]
They do cause a pitch up.

That is not what Boeing states in its condition for the memory items:

"Condition: Uncommanded stabilizer trim movement occurs continuously."

VESBOT states:
You're mistaken, "climbing" (or, put more precisely) elevator/AOA control always controls speed. Of course, under the likely MCAS scenario discussed, they did not have AOA control and the airspeed was running away from them.

And thrust always controls vertical flight path, so if they reduced thrust they would have only hit the ground sooner. In a desperate fight for altitude, "piloting" would dictate maximum thrust.

If the above is true, when you are ready for take off, try this:

Pump the elevators up and down until you has reached VR, then when you reach VR, shove the throttles to maximum to rotate.