I have added a couple players over the course in the past season who are currently my two best players, my "The general manager is doing everything he can to try to improve the team" rating has been between 3.5 and 5 balls most of the season.
I will note that I agree with your strategy, I am slowly improving my team as my SF training would become more difficult if I go all in for D3, so I keep plugging away at my arena and focusing on training my team (I have two trainees and a handful of guys who can get the extra little boosts in training once my two trainees get 48+). Hopefully my main SF will be ready to make a run at D3 in a season or two.