I have the Omega as well and have yet to run into the trouble you're having. I have notice that the triple 7 powder does tend to build up down near the powder load area and has made it tight when running my patch through. After every shot weather I'm at the range or in the woods hunting, I run a two of those pre-seasoned cleaning through my gun. The first one gets the heavy powder residue and the second one for a final quick clean of the barrel.
It's the way I've done for the last four years. I never have the trouble of the powder build up or the plastic sabot build up since I started doing it this way. When I'm heading for the woods I take about a 1/4" worth of pre-seasoned patch and I keep them in a sandwich baggie. T/C sells these in a jar that comes with 100 patches. Give it a try and I hope this helps