I also have this feeling, but from my limited experience with control systems you might want to try the simplest first.
There is a tremendous amount of variables to consider, and the analysis of how to take each into account is non trivial -- if you don't measure some variable precisely enough it might make the whole system less stable, the solution might get worse due to increased computational load, the conditioning might degrade, etc.
So with the number of controls they have and the predictive models available, I'm sure they're actually scrambling to refine their systems right now.
The thrust to weight ratio of a single engine firing is so high that they have no option but to fire at the last moment. Firing for longer would result in the rocket going back up, it can't hover.
