Update… Thanks again!
THE PET RESUME WORKED! I went on the tour, totally hit it off with the manager, and told her how much my friends love the place, and how much *I* love the place (seriously, it's gorgeous and the closets are gigantic), and then she mentioned something about "your dog" and I said, "Oh, I don't have a dog; I have a cat... what is the pet policy, btw?" She said, "One animal only, so you're fine if it's just one cat." I asked about "caged animals" and she was like, "Oh that's fine... but what kind of animal?" As soon as I said "rabbit," she was like, "Oh no, I'm sorry, absolutely no rabbits. No exceptions." Apparently when people had rabbits in the past, they peed everywhere and absolutely destroyed the carpet. So I said I understood, and offered to pay an extra deposit, and she still said no. Then I just started rambling. I pulled out the pet resumes and talked about how she's litter trained and NEVER unsupervised and doesn't EVER pee on the floor, and I clean her litter box constantly, and spayed rabbits don't "mark" just like neutered cats don't spray, etc. etc. etc. Then she said she might think about it. Then I went on and on some more, and started talking about how I understand her concerns because I've had a lot of trouble even finding a nice place that allows pets -- a lot of the "pet friendly" places are crappy, and it's hard to get into a nice place when you ARE a responsible owner, because so many people aren't and ruin it for everyone. And then I started pulling out printouts from the House Rabbit Society about litter training and the fact that older, spayed rabbits are easier to train and less likely to chew destructively (kinda like how dogs are less likely to destroy things than puppies), and I swore I'd keep her in the kitchen and put boards down to protect the floor if need be (not that it's necessary -- she really IS litter trained), and finally she said, "Ok, I NEVER make exceptions to this, but you've got to be the most responsible rabbit owner in existence... so I will make an exception." She asked if she could keep the resume (which of course I let her) because apparently she'd never gotten something like that before, lol. And she kept all of the rabbit info to read over. (She had a rabbit as a kid, but didn't know you could train them so easily.) So... I am super happy about this (I am in love with that apartment), but I'm still also scared because I have nothing in writing. I have to call her 2 months before my lease is up to actually apply. So I hope she doesn't forget who I am, or our agreement, in the meantime. (I wrote my name on the pet resume, so that when I go to fill out the rental application, assuming she still has that, hopefully she'll remember.) Honestly, I wish we could just move tomorrow. But thank you all for the excellent advice. (And no, I did not cry when she said no at first... although honestly, I was pretty close!)