What you call a "cuff" is what most people call a bladder. Unfortunately what it does is swell up in side the pipe and then simply jet a hole through the clog rather than actually removing the clog. They make an inexpensive tool that screws on the end of your garden hose like the bladder but it has swirling jets and a small spinning blade to cut through the clog. Harbor Freight has them for about 6-8 bucks and this might work better in your situation than just the bladder although you may need to use the bladder first to punch a hole through the clog.
To alleviate the grease problem it would probably help to flush the line on a regular basis with very hot (140 degree or so) water, several gallons at a time, perhaps once a week depending on how much grease gets poured down the drain. An enzyme drain treatment once or twice a month would probably also help. I think the one most recommended here is called Bio-Clean.