Running butt bounce even with compression

So I have a big butt. It's basically a shelf back there. I really want to run, but whenever I do it hurts. When my butt bounces, it feels like the meat is trying to fall down and slide off of my spine. I've tried running with compression shorts, triathalon/biking shorts, the works. Is there anything I can do? It also happens to a lesser degree with my chest and stomach. Heck, it happens with the elliptical if I try to really bring up the intensity. Is this just something I have to deal with until the weight comes off? Thanks!

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