This is what I did. Use a two pole switch, feed both poles with the 24v, output, one line to relay (contactor) other feeding light 24 v bulb. You may have to come up with a ground for negative side of bulb. Use a little imagination, it can be done without running another wire to the shed...
Oiless compressors have a finite life. The Teflon ring sacrifices it self to the brass cylinder liner. You can repair them. Personally, I'd bite the bullet and buy a "real" (read, oil lubed) compressor. One that the motor is not fraudently rated at 6 hp. A "real" 6 hp motor uses about 30...
Circumstances change, people change, and move (in and out). Sounds like a long term nightmare to me. My suggestion, look for a bigger lot with no encumbrances.
I never saw the end of your furnace replacement project. Did you, in fact, do it yourself?? Or, did you (successfully) repair your existing furnace?? Faced with an aging furnace, I'd be interested to know. My inclination, for myself, would be to attempt to locate and install, the exact...
I'd recheck your math. Check Machinery's Hand Book?? I'm working on a similar set up, Curtis D 96 compressor. Factory recommends 6" motor pulley, compressor is 16". Preliminary test shows 5 hp motor using 25 amps. 5 hp is nominally 27, wasn't up to 175 psi yet.
GE quit making those motors because they were bulletproof, couldn't sell replacements. Replace those microswitches, atypical starting switches, atypical centrifugal mechanism. Likely double row ball bearing on shaft end, single row on the other end. Just because it's me, I would rplace both...
Arguably, gold is the best conductor. I used to coat the contacts in the rheostat on my Lab (think, sewing machine) belt engine in the dental lab with 450 fine gold solder, seemed to hold up well. 450 fine is not pure gold and has a lower melting point than pure gold.
Generally speaking, air compressors don't do well with artificial three phase. The inrush current is enough to overwhelm the out put of a VFD, especially 7.5 hp. Not saying it can't be done, would require an expensive(read, sizable) VFD. And a sizable circuit breaker . Jus' sayin".