Yup. Madden is fundamentally broken in this aspect. You have to sim free agency and the draft in order for it to not be monumentally time consuming.
It's pretty irritating since it is actually a step back from previous games. (Where you could also switch teams during franchise mode)
What I do (since you have to control all 32 teams just to get the coaches using the correct defenses) is get all the players I want in free agency and make sure you make them an offer they can't refuse, then sim the first day. Hopefully they sign, then get of the FA screen and sim it from the off-season menu. That gets you what you want and allows the computer to sim the rest without you having to OK/Deny every single signing.
Then for the draft, I sim each pick until I make my first round pick, then just sim the whole thing. This does two things: Makes sure you get at least on good player each draft (as you should know who is good in either your imported draft classes or the pre made classes by now) and keeps balance in the game by drafting six other sucky players for you every year.
That seems to be the best way to handle it if you have to control all 32 teams.