I hope I'm not going to confuse similar incidents but I seem to recall from the AeroPeru accident that they managed to get up and away but it was getting down again that was the trouble. It's easy enough if you've got an ILS to slide down; in this case it's just a matter of getting on the glideslope, setting the recommended power settings from the book and erring on the slightly fast side if confused. As already stated, there's other information around ATC, IRS groundspeed etc, so it's not all lost. If you exceed a flap speed and damage a couple of panels, hey ho, at least you're alive. However, if there's not an ILS you can use (or PAR) then it becomes a whole new can of worms. Is it possible to descend over the sea and use the radalt until you can see what's underneath the cloud? Is it possible to have a shepherd aircraft (military) join you in formation and (a)lead you in the right direction and/or (b)give you the information you need; speed, altitude etc, these things would go through my mind but I am lucky enough to fly in an environment that has ILSs all over the place.
I believe this incident was the catalyst for getting attitude/power settings put in the QRH. I'm not going to argue if somebody tells me that ain't so but I don't recall them being on the 757 until after this accident (it may well have just been my company at the time).
As Rainboe says, the din of clackers, shakers etc going off cannot be ignored. It only takes a climb of a few thousand feet with the pitot tube blocked and the poxy overspeed warning goes ballistic and this is distracting enough to seriously affect judgement. As good a reason as any for most companies collaring the appropriate CBs, so you can pull them and get rid of the spurious noises as soon as possible.
What about opening the DV window and using the escape rope as a 'sounder' ike the ships of old? "How many fathoms till touchdown number one"