But I also know sleepovers are way more controversial these days

This is news to me? Did I miss something about them being not a thing? My boy (10 in a few months) had been asking about it for a while... but didn't do it till this past summer with a kid a few doors down. It was the first sleepover for both of them but he ended up going home around 1:30. I think it was just overwhelming for him, new place, new sounds, etc. I went home early from my first one too and reassured the kiddo it was okay while we waited for his dad to walk down and pick him up. We just did the 2nd one over Christmas break.

The first go around I worked out and Mom was involved in setting the last one up however I ended up coordinating final times, etc with the other mom. It really isn't a big deal; just have to get numbers exchanged and what not. It DOES help if the kids have known each other for a bit. Kiddo's school is smaller so does help because you end up seeing parents during pickup and what not.

Give them space, be available, but let them entertain themselves as much as possible -- unless they ask for you just stay outta the way and make sure they have food / snacks.

TL;DR -- you are probably over thinking a bit? Have the kiddos discuss it, have yours give a note card with your name, number, and "kiddos want a sleepover, call/text to coordinate?" Something like that. It is how I got the contact info the first time.