Yeah, dunno what's up with your prob. High rise shouldn't have anything to do with windage limitation, wouldn't think.
I've been using a no name (too cheap to even say "made in China") 3-9x40 on my Mini 14, seems to do okay, although I think the reticule may actually be losing index sometimes.
Anyway, these are just the standard Ruger rings shipped with the Mini, not high rise AFAIK, and yet the 40mm objective end clears everything.
One thing with cheap scopes you probably have noticed - you can get either adjustment turned too far for it to actually work logically anymore and you have to go back the opposite way you want to adjust for it to "catch up".
I don't know beans about all this like MikeGideon does, but I sure would borrow a scope before I went further with diagnostics, myself.
- OS