It would be nice if one did not need to scroll all the way to the right to start a new training. It is a lot of scrolling these days.
Likewise, what about a menu in the fort with all the LPs? Like a little front page with all their heads and you can tap to go straight to that cell. I hate scrolling all the way along when the LP I want is in the last cell. It could even have a little symbol to indicate if an LP is exhausted, rested or training.
I like both suggestions that have been made. - make the cells switchable so you can rearrange them - make a frond page with all of them. The first is probably not the hard to make in the game That second would alter the look and feel of the cells a bit more, which might not be desirable.