I've played on a lot of really old, badly out of tune, missing key top uprights in Sunday School. Most from the 1920's, forgotten brands. Most had pedal problems due to rough moving by the deacons. None of them had problems with double striking or more than one different key rest height, except for the missing ivory tops. It sounds as if this piano is a refugee from a conservatory or other place where it was practiced intensively, wearing out the felt pivots and wood pieces. Run, hide, this is horrible.
Any random upright you pick up for $50 plus $200 moving expense, should be better than this. The main thing to watch out for on those is that it is not a model where the glue holding the joints together on the wood parts is failing.
For maybe $200 you can pick up a post WWII console with less than stellar tone, but adequate mechanical performance. I find the ones from the fifties have better low volume consistency than the bargain brands from the nineties. At this price point, speed of action has nothing to do with the price. You can check speed of action for yourself, and get a bargain on a forgotten brand with no status on E-bay.
Get out there and look around. And find a friend with a truck, and spot a piano dolly you can rent. Better pianos than this are going to the dump every day. I've seen spinnets at Goodwill for $40 that were much better pianos than this. One of those little 36" spinnets weighs about 150 lb and will fit in the trunk of my car on its back. Use 2x8's to slide it on its back over the trunk lip. (I did that with a $137 Hammond A100 organ from Salvation Army, about the same size as a spinnet).