Some food for thought.
In my age group 45-49, the world record holder for the fastest 200m in competition did 11.3 seconds without using any banking or draft, at sea level (Manchester, UK). He has smallish legs and generates his speed at fairly high cadences. The second best sprinter in the world has large legs and does absolutely no weight training-he does a good amount of sprinting up hills in training.
If you're going to do squats you need to do plenty of core strengthening and upper body too so you can support the forces generated by your legs. If you sprint hard up hills the supporting muscles should get trained to their appropriate levels.
I think your earlier calculated wattages (and maybe forces) were too low. I do uphill sprints for 20" in 53x15 and the wattages are usually 960-1100, for 6 to 9 repetitions. Somebody else already mentioned the neurological adaptations. By sprinting at fairly high force, for this many repetitions (pretty much to failure mode) I think it's likely that you're engaging about as many motor units as possible.