Whining noise when attempting to start?

This is going to be a lot, but there's a lot of backup story leading up to this particular situation.

A few years ago, my Miata would start to do this wonky thing about maybe once a month. When I would start the car, it would turn on, but the engine would aggressively shake (mind you my motor mounts are loose but that's not the problem) and the car seemed to not want to shift? It would stay under 20MPH and red line no matter how slow it would go. I started to notice that turning the ac on or using anything like steering, rolling windows down, or putting the car in reverse/drive would make it significantly worse. Back then, it would only last about 10 minutes before I would hear the car rev up on its own and "correct" itself. However, over the years it began to not only occur more often, but also occur longer, getting up to 30 minutes before correcting itself. I've taken it to the mechanic once, where he replaced the fuel injector (don't know why) and then a second time where he had to keep it for months because he could not figure it out. Finally, he called me back explaining he had fixed it, and if I'm being 100% honest I have no idea what he even did, I'd have to find the receipts. But not even a day after I picked it up from him, it did the same thing at a car wash. I had to wait about 30 minutes before it was corrected to drive it home. Once I got it home, the next day I tried to crank it, it wouldn't start. And now here we are. When I try to crank it now a few months after the fact, it makes a rather loud whining noise.