You could solve the troll problem tomorrow
If you just gave players the ability to choose who they didn't want to queue with. And to me, it's completely reasonable. You want to "ban" every person who doesn't play to your standards? Fine, have a 50 min queue time. For me, it's pretty simple. I dodged 2 games tonight, one in which a toxic person (in the lobby) off-meta picked a champ and I said "I'm not doing this for my first game tonight."
I played a game after my 6 minute timer. Took a break. Hopped back in, and I got the same guy in the lobby who was jungle. Tried to take Yas but the enemy banned Yas. Tried to take Nasus but the enemy team picked him, and then finally went IN meta. But the support was acting up and I just dodged. Looking at his match history was confirmation that this 30 minute timer I'm on - because I didn't want to waste time and LP - was sadly the right call. Now I'm waiting for 30 because this guy chose to be a jerk. Ramifications? Probably not.
Not that it matters, but I work full time and am in grad school part-time. Blowing 30 minutes isn't efficient. I play this game to relax and instead I'm now weighing whether to stay up late and roll the dice on tomorrow's commute for a match (with maybe no obvious trolls), or just go to be now. Why does it have to be this way? It really doesn't. But the indifference toward the low brackets, brackets where everyone "can climb if you're good" has to deal with these people down here with zero help from management.
If I wanted to clean up other people's messes with no help from the people profiting from it, I'd find a second non-profit job.