Please reconsider your statement on roll inertia. The B737, depending on the version has adequate aileron authority, other than below crossover AOA (it is not speed, please stop calling it speed, the aircraft doesn't care about speed, it only cares about AOA... well, yes, speed for... anyway, crossover is not a speed, it is an AOA).
Not sure where the speed comes from.
Once a rapid roll has been initiated, neutralising the roll control input will cease the roll, quite promptly. An opposite roll control input will reduce the time to go to zero roll rate, however the B737 will damp a roll rate in about a second, so at the most optimistic and enthusiastic roll rates, say 40 deg/sec, you get an additional 20 degrees of roll approximately. If you used any opposite input, then the 40 deg/sec rate will be removed almost instantly, coffee will spill in both cases, more in the second.
The B737 ailerons are effective through to stall, and actually below, but with caution, as in most aircraft, large aileron inputs in the stall or above stall AOA can lead to a roll reversal. Spoiler roll control remains effective. Crossover AOA relates to the relative authority of the rudder vs aileron in roll control. At normal speeds, the ailerons are adequate. At high speed, the ailerons respond normally. Above VNE/MMO the ailerons generally act normally, however, at extremely high speed excursions, large aileron inputs can result in roll reversal, that is in the 450KCAS and above range, and at that point it is time to stop playing about. There is a single set of data that shows a roll reversal occurring, and it did not end well, and the whole trainwreck was caused by the Pilot-In-The-Left-Seat-Being-Paid-To-Nominally-Be-In-Command.
Roll rate is determined by control deflection, (aileron/roll spoiler/rudder, AOA, CAS, and speed brake effects on lift distribution. Thrust asymmetry gives a secondary roll... which is what the AP was managing in this case, until it couldn't. Roll rate can also be affected by any mis scheduling of a FBW gain that has erroneous sensor data such as actual flap deflection, Roll damping has additionally density effects. (not the whole answer, it is the bits of interest)
Of course, the B737 does have sufficient aileron authority. That's not the issue.
Though, when you have a large aircraft (roughly 3 times the wingspan of a small aerobatic frame), your inertia forces will increase significantly, because the forces/energy are with roll-rate^2 (IE tip-roll-speed).
Aerobatic aircraft tend to have 180+ degrees/second roll-rates. A B737 doesn't do that (the report states 49 degrees/second) and IF you could try 180+ degrees/second, you'll rip off the control surfaces, the engines (Gyroscopic effects), the wings, etc. There was a nice article on PP, about B707's crashing (presumably after barrel roll attempts), and/or engines departing the frame. When the rotating engine core is not perfectly aligned with the roll axis, but wobbles around that, and with 4 engines also circles around the roll axis, the gyroscopic forces on the engines are enormous. Enough to tear-off the whole engine, which happened.
With 49 degrees/second, you get 3.5 seconds to inverted and probably another 3.5 seconds to get blue up again. Which nicely matches, with my earlier graphic reading.
Of course, when you approach the perfect blue-up situation, it's tricky to have the roll stop at that moment, so the roll somewhat oscillated around the desired position, so be it.
At 07:40:05 UTC:
- the control wheel trim switch activated and A/P disengaged,
- the aircraft rolled to the left with the roll angle of about 49°,
- the highest aircraft altitude recorded was about 10,700 feet, thereafter the aircraft continued to descend until the end of FDR recording,
- the left thrust lever decreased to a position of about 8° and the N1 speed of the left engine was at about 34%,
- the right thrust lever position and the N1 speed of the right engine remain unchanged, and
- after the A/P was disengaged, the control wheel was deflected to the left for four seconds and recorded deflection value up to 18°.
1:25 after the anomaly, the crew didn't comprehend what had happened. The AP disconnected because the trim switch was actuated. Once that happened, a condition that the AP had about 1/3 RWD input of the ailerons, with the aircraft already rolled to the left "inexplicably", the pilot puts in up to 2/3 LWD aileron for a short period.
"BANK ANGLE" GPWS Mode 6 triggered 2 seconds before this....
With the control wheel obviously significantly out of neutral, it is strange, they did input only a short trim-blip. Given the violent control wheel movement after the short blip, it suggests, the control wheel wasn't really in firm hands. Strange and gives me the impression, the trim-blip was unintentionally. It could very well be, the trim-blip did happen due to the control wheel acceleration or just the movement and touching something. The fact that the AP kicks out just at the same moment of a trim-blip, does not imply a cause-action, it could have happened simultaneously, with an opposite cause-action as normal logic determines. The graphic time-line resolution seems to be "only" around 1.5 seconds.
Not to say, I can't imagine a pilot doing a one-finger trim-switch push and not having the significantly out of neutral control wheel firmly in his/her hands. Not to say, the way the pilot reacted to the roll (not "fighting" the roll, but helping to roll through the upside down position towards blue-up) and realized wings-level that fast, implies a lot of flying experience, a pilot with military / fighter-yet experience ?
The control wheel deflected to the left for 4 seconds is understandable. If you want to get your blue up as fast as possible, you are going to help the continued rotation, the moment, you are already at or approaching 100% upside down. When looking at that trace, I don't see things which do surprise me, on the contrary, they pretty well understood what was happening AND what to do about it (continue the roll and stop "around" blue-up).
Unfortunately, they ran out of height to finish the recovery.