I'll make an update, in case someone googles this in the future. I disassembled the tilt cylinder in place, and replaced every seal. This wasn't too bad of a job. The worst part by far was getting the gland nut free. I ended up bringing the boat to a hydraulic shop, where they had the proper pin spanner wrench, and it broke free with a little elbow grease. There is another fitting you need a pin spanner for at the lower end of the piston, but I was able to fab up a tool to get that one free since no shaft is in the way.
Anyways, back to my original goal of changing out the fluid. You can indeed remove the manual tilt valve shaft, however there is a plastic flange that is just a hair too big to pass through the hole in the right bracket. I was able to reach in there with a die grinder and grind it down slightly so it came out. With that shaft out, you can dump lots of clean fluid in through the fill neck, until it comes out clean on the other side.
Reinstall the manual valve shaft, and begin the bleeding/purging process. This took some time to get all the air out. Eventually, while taking breaks to ensure the motor didn't overheat, I was able to get the tilt and trim to function correctly, with no leaks!
Then I drained the fluid and flushed it again. My goal was to get crystal clear (red) ATF with no contamination. Lots of bleeding/purging and topping it up and I am finally happy with my tilt/trim, and the fluid is very clean.
Rob