My experience regarding "handling the big jets" admittedly consists in having read the book, but to my understanding Davies puts a strong emphasis on stall avoidance (e.g., p. 128 concerning "advice on what to do about stalling, there is only one thing that can be said -- don't!") and the numerous important differences between light piston airplanes and big transport jets. This just makes me wonder whether VFR aerobatic training in a light and extremely agile and responsive aircraft would be one of the most beneficial approaches to LOC scenarios in airline flying.
Similarly, C. Sullenberger himself does not seem to think that it was mainly his glider training and stick & rudder skills in light aircraft which helped him in his successful ditching:
Air & Space: Did you flash back on any of your experiences as a glider pilot? Did it feel natural to you?
Sullenberger: Actually not very much after the bird strike felt very natural, but the glide was comfortable. Once we had established our plan, once we knew our only viable option was to land in the river, we knew we could make the landing. But a lot of things yet had to go right.
I get asked that question about my gliding experience a lot, but that was so long ago, and those [gliders] are so different from a modern jet airliner, I think the transfer [of experience] was not large. There are more recent experiences I’ve had that played a greater role.
One of the big differences in flying heavy jets versus flying lighter, smaller aircraft is energy management -- always knowing at any part of the flight what the most desirable flight path is, then trying to attain that in an elegant way with the minimum thrust, so that you never are too high or too low or too fast or too slow. I’ve always paid attention to that, and I think that more than anything else helped me.
(Source: A&S Interview: Sully)