Couple of comments:
The FH-TX500 that was quoted to you is not a very high-end hub and has minimum dust/weather sealing. The hub on the prebuilt is probably similar, you should at least inquire on what hub is used. Unfortunately, Shimano has reduced the models that they sell for MTB 135mm rim brake wheels, most are disk brake hubs now. Don't know if they have any non-disk brake hubs in 40H. The FH-T610, in their touring/trekking, is probably a better option.
The FH-M770 is not 24 years old, it is more like 15-18 years. To check if it is having issues, at least remove the wheel from the bike and turn the axle by hand & feel for any roughness or sticky points during the rotation.
Any rim marked as 622 is the wrong size. 622 is for 700C road tires or 29 inch MTB tires. 559 would be the correct size for 26" tire, as you note about the tires you use. This is the size of the rim or tire bead set, where the tire hooks into the side wall on the rim.