The old procedure was
Control Column - Hold Firmly
Autopilot - Disengage. Do NOT re-engage.
Control pitch attitude manually with column and electric trim.
If runaway continues, stab trim cutout (both) to cutout.
http://www.b737.org.uk/images/runawaystab2000.jpg
The new procedure is not that much different.
With PK-LQP - previous flight it took 6 minutes for them to get to this procedure - and it was suggestion of a dead-heading pilot. This resolved things. Despite going through this exact issue on previous flight, the next flight takes off, same issue develops because of underlying maintenance issue, they were dealing with this for 8 minutes, 28 activations of incorrect trim but with a fatal outcome.
Yes, MCAS was a bad design, yes it increased risk. I'm not sure it was a "nothing could be done" type situation. Better maintenance? Better communication between flights? Stab trim cutout earlier if you don't like how the automatic trim is working?
Airbus has historically pushed more automation / flight protection. My own suspicion is Boeing will go that way as well, ie, human in loop model they had (where human fixes the computer going crazy) just doesn't work well especially for folks flying these big jets without much earlier GA / manual flying time.
For example, in the US, a pilot would have done lots of manual flying on small planes first, and so might be a bit less automation dependent and better able to take over when computers go crazy. Also more hours before you fly the big jets (think 1,500 hours flight time). Usually a 4 year degree.
Overseas, you can come off the street and be flying a jet with 200 - 240 hours of time including sim time? That is a TON less flying time, probably very very little manual stick and rudder flying. A fair number of saves in the US have come from folks with great stick and rudder flying experience, even things like glider experience you just don't have overseas.
There usually is something called differences training for variants like this. Wouldn't cover MCAS, and is usually brief, but not normally zero. I'm surprised they did zero differences training if that was the case - that is very unusual. You've got to do normally at least an hour or two. A new variant is not unheard off, 737 probably has something like 12 variants under one type certificate. I would check your source there that no differences training came up.