It's a combination mechanical (brackets, cables, etc) and electronics job (pin-outs, connecting to inputs and outputs, etc. And it has to be right, otherwise it can jam the flight controls or disconnect the flight controls as failure modes.

If it works well today and the install looks neat and organized, I'd just pay the bill and be happy about it. No avionics tech would have agreed to a 20 hour flat fee, you probably got a bill right in the average range. If the work is above average, mission accomplished.

I would be more upset about the 2 months downtime.

My neighbor had one installed and had equal hopes of a 20 hour install.... it took an experienced shop more than 30 hours. I don't think it's at all unrealistic to take 38 hrs. I realize that it's hard to accept the install cost about double what you expected, but I don't think the shop is out of the ball park. The 2 months downtime is what would have bothered me the most. At least it's a good time of the year to be grounded. Enjoy the new autopilot!

Best

It’s been my experience that nearly every STC’d product (TKS, autopilot, aux fuel tanks, air conditioning, etc) that is more complicated than a light bulb, if you take the time the manufacturer says it will take and double it you’ll more often than not be within spitting distance of the actual install time, counting all the paperwork and check-out.