OK, so someone like AC may give you some more food for thought on shoes specifically, but I'll give you my take on what you've said.
I was going to get rid of him.... both said farrier #2 was great and was doing a good job on some very bad feet.
Curious what made you want to/eventually ditch him then?
Farrier #3 said that he needed to get her heels off the ground and wanted to take her rear shoes off. The goal he said was to have her barefoot all four within 3 trims if he could.
Yes, if her heels are that crushed, relieving them from ground pressure, such as 'floating' the heels can be part of the 'fix' to allow them to relax down & return to a more upright structure. With wedge pads, &/or if the frogs are otherwise receded from the ground, frog support is important. I'm imagining by the look of it, her heels are also very contracted & weak too though, so I'd definitely be getting some support & protection under them, which will also help spread the load on the heels.
If he wants her bare, why does he believe shoes are necessary now then? I ask because I have found it's generally easier & quicker to address run forward feet & crushed heels without shoes. Can be a long job though - possibly far more than a few trims, and depending on how long/how bad the contraction & crushing, you might never expect them to become that great.
the goal was to keep the front shoes on as long as able since he didn't want additional holes in her feet.
Disagree with that 1000% especially as her feet are already run forward to begin with. The longer they go between trims, especially being peripherally loaded, the more run forward they'll become - or at least he will be chasing his tail having to 'correct' things each trim, rather than maintaining & progressing gradually. Nail holes are a minor 'side effect' of shoes, especially compared with overdue trimming.