! Could my water pressure be too high?
No.
so far I've spent a bunch of money and have made no progress! $15 new seals, $40 new spindle, $26 seat kit, $21 seat removal tool -- $102 into the hole and now it looks like I need to replace the whole thing...
A review of Symmons warranty would have told you that the valve was warranted for life.
Warranty Information
A review of the installation instructions would have provided information you needed to request replacement parts (free) including the seat removal tool.
It is unlikely that a valve of the quality of a Symmons would leak due to defective parts (washers and seats) after only 3 years. But stuff happens.
It is illogical that a leak would continue after replacing the critical parts (seats and washers) unless you mucked something up in the process. Not saying you did, just that we all do occasionally. Also, it appears that it would be difficult to muck up replacing the seats and washers, after all it's a plumbing valve, it is not a Swiss watch.
Not only is it illogical that you would have a leak after replacing the seats and washers but it it is totally illogical to have the leak after replacing the entire valve.
Obviously, there must be something else going on. And no, it is not the water pressure. Your pipes and valves are built to withstand far greater pressure than you could ever produce in a domestic water system even if you were trying to cause a problem.
As to water pressure. You didn't say but I get the impression that one side (hot or cold) that leaks, not both. Perhaps I am wrong. Water pressure (static pressure) in a domestic water system is always equal, not only between the hot and cold sides but through out the system. So no, the problem is not water pressure.
Have you considered contacting Symmons for technical assistance?
If I were going to guess as to what the problem is, I would guess that you have some debris trapped in the system. If I were going to guess what the debris was, I would guess that it is solder. When soldering copper pipe if an excessive amount of solder is used or the joint is over heated, the hot, melted solder can run down inside the pipe. Hot solder will not stick to a cold pipe. It can then lay in the pipe, sometimes for years, until the water flow moves it to the next available valve. I have a hose bib that began leaking after about 10 years. I remove the stem and flushed it out. The hose bib was fine for a couple more years. I had to repeat the flushing. Apparently I didn't get all the solder out. It has been leak free for two or three years but I may have to repeat the process in another 10 years except I probably won't live that long. Clearing the pipe can be difficult if there is a vertical section of pipe near the valve. The flow can move the debris to the valve but it can then fall back down the pipe when the flow is stopped.
"Ifn't it wus me", I would remove the spindle, and because you have had so much difficulty with this valve, I would also remove the seats to provide a larger opening in the valve, and flush the piping well. I would turn off the hot at the water heater and flush the cold side, then turn the hot back on and flush both sides.
Good luck.
Just as an aside. I put a new water heater in for my neighbor over the weekend. I had some difficulty. She now reports that she hears a squealing when using the shower. Obviously I have some solder in the valve. I intend to go over and flush the shower valve as I have described, just as soon as I have another cup of coffee, or maybe two.