If you have a dedicated room that's totally black anyway, you can just run that cabling along the ceiling coming out of where it's at now 6 feet forward to where the projector is at and hide it with a painted black channel. You'd probably never see it. My room is a pitch black cave and I have cables hidden along the sides of the walls. No one can even see them. Plus this is not a permanent install you could undo it at anytime if you hated it.
I ran a black CAT5 cable along the baseboard, up the black wall, and up to the projector for IP control no one can see that either. I'm sure you'll benefit more from the increased lumens of moving forward vs the occasional seeing the black cover of cables when the lights are on and the projector is off. Of course if this is a living room, forget what I said. The cosmetics will matter a lot.
Video: JVC RS4500 135" screen in pure black room no light, htpc nvidia 1080ti.
Audio: Anthem mrx720 running 7.1.4, McIntosh MC-303, MC-152, B&W 802d3 LR, B&W HTM1D3 center, B&W 805d3 surround, B&W 702S2 rear, B&W 706s2 x 4 shelf mounted for atmos, 2 sub arrays both infinite baffle: 4x15 fi audio running on behringer ep4000 + 4x12 fi audio running on 2nd ep4000.