It may be time to consider making the move. I have a road bike with Shimano RX100 derailleurs. The way I remember which direction to tighten or loosen spokes is by thinking of the spoke nipple simply as a nut. In other words, clockwise to tighten, counter-clockwise to loosen. Work with the spokes closest to you and your attempts at wheel truing will be happier.
Wheels are always stronger when their spokes have uniform tensions.
It does sound like the upper limit screw on your rear derailleur needs adjusting. And your solution of backing off that screw sounds correct too. The more you tighten a limit screw, the more you limit the derailleur's travel in that direction. Backing off that screw extends the possible travel. On modern derailleurs that don't indicate which screw is which, the screw that's HIGHer off the ground is usually for the HIGH gear.