I have the same sources for all games, with separate scenes for each game, as you mentioned, I've always had it like that. I'm usually pretty good at spending the least amount and generating the highest gain in return.
I can't help but think OBS-Studio is just designed poorly then if it handles worse than OBS Classic(or so with the same settings, it's a hassle finding the specific settings to use), I mean, apart from sharing the name, it's really the same program, just "upgraded". Like the saying goes, why fix something that isn't broken, it would of been worth while just adding extra functions to the classic like what's available in studio, little things like "fade" so on and so forth instead of revamping it entirely regarding it's software, and ultimately, making it somewhat worse, at least for me, I can only imagine for other's too.
I would go back to OBS Classic in a heartbeat, however, knowing it's missing some great extras that studio has to offer would be depressing, only other alternative is XSplit, no idea what that's like yet but I'm probably going to find out, lol.
EDIT: I just did a test stream with lowered settings, 30fps, 8bit not 16, and same lag, seems to be cpu usage in obs.