For me the problem with blitz as a learning tool is that you don't understand what is happening as it's happening, thus the playing experience is of questionable value. In long chess a complex sequence of moves might become easy to find in a fast time control when you study it long enough and break down its nuances.
In a fast time control, if I was confused by a complex sequence before, since I never truly figured out what was going on, I'll probably be confused by it again.
Of course you could analyze positions you got in blitz very deeply, but I think long ones are more relevant because the insight into your thought process as you go over the game is much deeper.
Ultimately, you can make an argument for blitz chess to improve your chess, but although I respect the points made, it's still a little unconvincing as a whole.
Looks like you don't really need any suggestions on blitz and bullet chess.
Just remember that the goal of chess is to have fun!