There's a very particular (and somewhat streamlined) process for doing Field Approvals for non-AML IFR GPS units that have an existing single-model STC. Garmin's install documentation for those units contains a "sample" AFMS (which requires little to no revision) and a checklist for the IFR "checkout" that has to be documented per the FAA field approval guidance. You don't have to write an AFMS from scratch (and 10 hours to work with Garmin's "form" is bonkers). Garmin's STC permission is there to allow you to use that STC data as "acceptable" data to support your field approval request (if the STC were applicable to your actual airframe, the STC data would be "approved" data). I installed a GX50 about 6 years ago as a field-approved IFR navigator in my old Twin Bonanza. Was a very simple process, but it took the FAA a couple of months to approve my AFMS (for no particular reason).
But what you're going to find is that almost no A&P nor any avionics shop wants anything to do with a field approval, even if a straightforward and streamlined one. It's not hard, but it's a black hole with the FAA in terms of how long they'll take to actually review and approve the AFMS (which can be approved at the FSO level, doesn't have to do to the ACO like most field approved AFMS do). It does take some "administrative" (paperwork) time that most A&Ps don't like to charge for because customer's don't like paying for it. So to avoid that rift, they just avoid doing field approvals. Why spend the time messing around with something that is just going to make everyone upset in the process, vs. spending that time working on a "bread and butter" project (like annuals, etc.)?
All that said, YOU can do a lot of the legwork for the field approval if you have a cooperative A&P and the time/energy/inclination to get into the paperwork. Other than "custom," there's nothing stopping you from interfacing with the FAA directly to obtain the approvals you need, so long as your A&P will sign the necessary forms and cooperate with you. My A&P had almost no direct interaction with the FAA when I got my field approval (or when I got a later field approval for a G5 for an install in an aircraft not on the AML).