I do the same with my 10g cooler. I never had a stuck sparge with my dome false bottom, but I wanted something easier. I use a false bottom in my keggle because I use a lot of whole cone hops, and have a pump on my system. Works out really well.
I use this bag in my cooler:
http://www.brewinabag.com/collections/frontpage/products/the-brew-bag-for-coolers
IMO, it's the toughest bag available, and a very reasonable cost. They also have keggle size too. You still need an expensive false bottom if you are direct firing though, or you will melt the bag. The owner of the website is surprisingly local to me, so I met him at his house, and ended up talking beer for over a half hour. Lol! Very nice guy, and an hbt supporter. When I need another, I'd buy from him again in a heartbeat.