I went in and talked to the assistant manager, D., (B. the landlord guy is on vacation), and she was very positive about our situation. I said I gathered we needed to amend our lease to include Greg, and she said she would talk to B. about it. They don't usually allow 3 adults in an apartment (though she confirmed that our neighbors have three adults), and it mostly has to do with the cost of utilities. They're now splitting out utilities from rent on new leases, and I told her we'd be willing to pay, y'know, 50% extra on the utilities, and she said that was good. She thinks we're great tenants, and they would like to keep us.
She said she'll talk to B. on Thursday, when he gets back from vacation (because she doesn't like to bother him while he's on vacation -- I said, "yeah, that'd make him crabby" and the maintenance guy said "he's crabby all the time!" and they both laughed), and tell him that I'd been in to talk to her about it. She gave me a lease application for Greg to fill out. We'll have to do the standard $25 for background check; I mentioned that he'd pass the criminal check, but maybe not the credit check, and she said that wasn't a big deal because we always pay our rent and pay it on time, so the credit check isn't important for adding somebody to an existing situation.
But it seems like she's really rooting for us, and the no-three-people rule is mostly about utilities, and since we're willing to cover the extra cost, I think the odds are in our favor that it'll all be okay. Our rent may go up a little, but y'know what? That's okay.