First, this:
I mean really. It seems simple enough. Punk is simple. Rush is complicated. There are billions of songs, bands and genres between the 2. Shouldn't be that tough to find a middle ground. Right off the top of my head (cuz for some reason this song is stuck there).
Tons of classic rock fall into that category also, if ya want something with a little more substance. Any Sabbath, Zeppelin, Aerosmith... they all fall right between Rush and Punk.
Then this:
Drop $40 on on Transcribe, or find a free music slow downer that works well and work on having some patience and persistence. Take a Rush song that's giving you a problem, take a small section, slow it down RIDICULOUSLY to a speed that you can play it perfectly at, and then keep playing it over and over and over. You can use a metronome once you have the notes down. In between each practice period of playing it ridiculously slow, you can raise the tempo a notch and see if you can play it perfectly a little faster. What happens when you do that is you develop muscle memory. Your fingers memorize what you're doing as opposed to your brain, and you'll be playing the tunes effortlessly. I'll add also to start with one of the simpler Rush tunes. Spirit of the Radio's opening riff is NOT a good starting point.
It takes commitment and patience though. It ain't going to happen overnight, but it will happen faster than you might imagine. So long as you don't try to RUSH the practice and play things at a faster tempo than you can play perfectly.
I promise.