Sex Slider, Shag-A-Rama!

Quinn and Rembrandt, along with their two female companions, slide into a world where video surveillance is omnipresent and sex is forbidden to all but the elite. Naturally, they run afoul of that law almost immediately and the girls are captured by the sex police. Quinn and Remy flee and luckily manage to fall in with a resistance group. Together they must rescue the girls before they're either, as described by Victoria the rebel commander, "brainwashed to destroy all thoughts of sex" or "made sex slaves for the rich and officers." Plus there's that pesky countdown timer. If they miss their slide window they could be marooned in this dimension and never find their way home.