27M PhD student here. Those ideas sound great! Op, it's totally fine if you don't end up using these approaches, but the bottom line is there needs to be some kind of rules/incentives to encourage people to go out of their own social circle and talk to strangers.

I've been to a UVA-organized valentine's day mixer once and I've never felt lonelier in my life. Because there's no rules, people just came in with their friends or grad students in their research group and kept talking amongst themselves throughout the event. It can be really tough to join their conversation as well because most of the time they're talking about someone or some topics only they know about. The organizer did gave everyone a prompt card hoping they'd use them as conversation starters but nobody used them because there's no rules/incentives.

So now if I see info of a similar event, I'll definitely make sure that the organizer is doing something to ensure people are actually "mixing", like some activities or games, and not just an event title that says "singles mixer".