I am sorry to read about your problems in TN. One good option for you is to contact your local FAA Flight Standards District Office (FSDO) and ask if they have the list of Aircraft and Powerplant Mechanics in TN. There is likely an online list for these folks. Then use that list to start making phone calls.
Another option is to contact your aircraft manufacturer to ask them for suggestions.
Then another option is to research adult aviation mechanic schools in your area. You might find that a nearby school/college has a helpful program. Here in Louisville, KY, we have the Jefferson Community and Technical College, and then in Somerset, KY is another program. Not far to the north of us in Indiana are other programs that can help folks. Some of the college programs might be able to help you make your occasional repairs and that helps them to have planes for the students to work on. Realize that their time schedule might not be as fast as a rated mechanic, but their prices might be more in your budget. They all are required to abide by the same standards.
I hope that these suggestions are going to make you feel more comfortable that the awkwardness created by the mechanic you discussed. Certainly, if you have endless money, you could replace lots of items in your plane, but most people have finite budgets and that guy was not respecting your wishes. It sounds as if you are better off without him.
Tulsar is a Beech service center with a Part 145 Certified Repair Station certificate. Under that certificate, their repair technicians (i.e., those who don't hold FAA A&P certificates) can only work on the aircraft listed on that certificate, which is basically the Beech line and does not include Pipers. To add Piper to the list, they'd have to get all the Piper maintenance/parts/repair manuals and specifically train/certify their non-A&P technicians on Pipers, and they don't foresee sufficient Piper business justify the expense of doing that. However, they do have some people who hold regular FAA A&P/IA certificates and could work on/inspect Pipers under regular Part 65 maintenance authority if they had the manuals. If you were to purchase the necessary manuals yourself, they could do the maintenance and annuals on your Archer using your manuals. Call Mark in their maintenance department at 901-873-4780 and talk it over with him.
Another solution is to look around the airport and ask the other Piper owners (out of 61 single-engine airplanes on the field, I'm sure yours isn't the only Piper) where they get their maintenance done.
I am connected in the maintenance field around the Memphis, TN area and have a suggestion for you. I know a mechanic that used to work at Downtown Aviation with Matt who you were trying to get in touch with and he is well versed in general aviation while he does airline work from Wilson Air Center at MEM. The mechanic that could do your annual is Michael Grace and his number is (901) 371-7244. His website is http://www.vortexaviation.aero/ I hope this helps you out with getting back in the air! If not, let me know and we can go from there.
Anyway, thanks to everybody that helped with advice. Hopefully I will meet you guys at the field some time.
As far as the comment about Tulsair, I DID talk to them and they did explain why they could not do the service. I didn't think I needed to write a book here about what they were certified to do inspections on, just that they couldn't do Piper inspections. I have no problems with Tulsair and they are a great FBO at KNQA. I know it takes a lot to get everything certified with the FAA and they certainly don't need to waste the time and money if there isn't a market to justify it.
And yet Mark at Tulsair indicated their A&P/IA-licensed mechanics could do the work under Part 65 rather than their Part 145 repair station certificate if you provided the manuals. I guess Matt already has them, which saves you the expense. OTOH, there are good reasons for having the maintenance and parts manuals for whatever aircraft you own, and carrying them with you (at least in electronic form), as you never know where you might break and whether the maintenance facility where you're broken has the right manuals. I've got the Grumman manuals on the same iPad where all my flying materials are located so they go with me wherever/whenever I fly my plane.
I'm not sure what your issue is about this. The person I talked to at Tulsair said that they could not do the work. I asked him if there was anybody he knew of at KNQA that could do the work. He said that CTI will only work on their own aircraft and he did not know of anybody else at KNQA that could do the work. He suggested I check with the Total Air Group at Memphis International. Also, when I talked to him, I stated I had all logbooks AND MANUALS. I do believe an aircraft owner should have all manuals concerning their aircraft.
And yet Mark at Tulsair indicated their A&P/IA-licensed mechanics could do the work under Part 65 rather than their Part 145 repair station certificate if you provided the manuals.