[BirdWatcher]

I too play as both GM and manager but found some time ago that the micro-managing, in-game management aspects weren't my cup of tea (and that I'm probably not great at them.) Currently, with my fictional league, I am playing out all of my team's games, but letting the AI make all the moves (based, of course, on my overall directions- and I do control the starting lineup and pitcher.) I find this far less frustrating. Though I will jump in occasionally when I believe that a pitcher who clearly doesn't have it that day is being kept in the game too long.
But in my previous primary project (Colorado Rockies historical) I settled into a pattern similar to yours where I simmed day-to-day (usually playing/watching 1 game per week.) The game became much more enjoyable to me once I relinquished some of the in-game control.
Still, I would have a hard time giving that up entirely and just playing as GM.