I tried adding refrigerant, but without the compressor engaging, couldn't.
Yep. For a variety of reasons.
The instructions even stated that if the compressor didn't engage, try adding 1/2 a can - system wouldn't accept any!
The instructions 'assume' your compressor is capable of engaging (clutch functions and the electrical circuit is in good working order). Then further 'assumes' the refrigerant charge is so low that there is no liquid refrigerant in the system and as such...not enough pressure exists for the low pressure switch to allow the clutch to engage.
Guage was pegged way above the green 'fill' category, so not sure what's going on.
Since the compressor was not running there was no way to get a meaningful reading. With the unit 'at rest' the gauge was reading the 'static' pressure. The static pressure of R134a at 80° F is 88 psi. which of course will peg your gauge. So...until you verify that your compressor clutch is capable of working....you can't get a pressure reading (that is going to mean anything to you). No point moving forward.
I hate the thought of going to a dealer. They'd just want to replace the compressor!
Yes, unless you own the dealership or there is NO reputable alternative... NEVER go the dealer for A/C work. You might as well write on your forehead 'Please Rape Me'.
I think I may find an independent AC place to test it like you did.
Yes, it needs to have a set of gauges put on it, the circuit and the clutch tested. Go from there.