Hopefully some optimism for you! We just had a very similar story. We have two 17 year old cats (basic free cats - no special breed). August 2nd of this year they were both fine. One (Cocoa) was sleeping on the sofa. She jumped off (about 1.5 feet up onto carpet) and her legs just collapsed. She couldn't move her back legs at all. We waited a couple hours (just in case her legs were asleep or something) but it didn't improve.
Finally, called the all night emergency vet. We had just moved to the area in early July and hadn't even found a vet yet. It was 9 at night by this time, DH was in California, and I was home with the 3 boys. Finally put the younger two in bed, brought the oldest with me to help me and went. We waited about 2 hours (!) and the vet was less than encouraging. Started talking (sounds like your vet) about going to Madison (about 3 hours away) for MRI's, etc. By this time I'm exhausted, the cat doesn't seem to be doing any better or worse, so I tell her I'll call my vet in the morning.
Took the cat home, put her in the laundry room with food/water/litter and no where to go or try to go. Took her in in the morning and the vet (who I found then) did a bunch of bloodwork, CAT scans, ultrasound, etc. and of course came up with nothing. He felt it was some type of Vertigo, where the cat was so dizzy she couldn't walk, not that anything was wrong with her legs. Gave me meds and said she'd be fine in a week.
A couple hours later she started seizing - had 3 seizures during the course of the day. This made them rule out the Vertigo diagnosis and they began saying either blood clot or stroke. Put her on Phenobarbital and said come back in a week.
It was a rough week - for a couple days she really couldn't get in and out of the litter box or clean herself. We got the special newspaper (Yesterday's News) litter and a ferret litter box (very low and small) so she could get in and out. Got special wipes so we could clean her off. But in about 2 days it started to get better. She could eat, take the pills, and use the litter box herself (and clean off). Back to the vet who basically said he was sorry but she was barely showing improvement. He was confident it was a stroke, said she'd really never improve, and we were talking days, not months or years and just take her home and keep her comfortable.
Well, it's been almost 3 months! She's not back to 100 percent normal, but probably 90 percent!

We've locked off the basement (because she loved climbing around all the ductwork down there and I don't think falling would be good from that height!), but she can go the entire house. She goes upstairs, can jump on the chair and table, etc. She has more trouble with down and occasionally falls down when she jumps from a height (say from the table - she'll land, then tip over). She occasionally tips when someone moves quickly (say if you're carrying in a package and don't realize she's in the hallway and she tries to get out of the way).
But the vast majority of the time everything is fine. She's in remarkable shape for a 17 (now 17.5) year old cat, still knows and loves us, purrs, loves to lay in the sunshine, eats well and plays with her sister. We actually left her for 3 nights this weekend to go out of town - this was the first time we've left overnight since this happened! (Yes, we had a cat sitter who fed/checked on them twice a day). She still takes Pheno twice a day, but hasn't had a seizure since the first couple days. You know she's doing better because we find ourselves yelling at her again (Get off the table!) instead of being impressed (Look! Cocoa got on the table!)
So there's hope! We saw 4 different vets over the first week and they all said different things and offered expensive options and none of them were at all optimistic (kind of like "she's 17 years old - what do you expect?"). Yet here we are 3 months later with a cat who's nearly back to normal (just a little wobbly at times) with a lifestyle that hasn't changed much at all (she's always been an indoor cat). Keep your spirits up if the vets probably don't know what to do and hopefully things will get better! Good luck!