You need a "shelf" in the back. Gear goes below, dog goes on top. This should solve your problem, I'd think. Kilby makes one for the TJ that could be used as inspiration for a one-off fabrication project, or you could build a shelf on top of a Tuffy box or on top of a wooden or metal frame.
I've been meaning to make one for my TJ for years, and will probably finally do so this year - two pugs and a golden + camping gear and a wife...no way to take the whole family out in the Jeep otherwise. When traveling without another human, I can fit the golden and one pug on the passenger seat (yeah, you read that right) and they're surprisingly happy with that arrangement.
Dogs that are used to traveling in cars don't actually take up that much space, assuming you stop often enough to keep them from getting frantic. We routinely travel with all three dogs to visit the inlaws (560miles each way) with only a mid-trip stop for gas, with all dogs curled up together on 2/3 of the back seat of a Ford Focus. Our dogs are happy with the arrangement, but that's because they're familiar with car travel and with being lumped together alongside luggage!