I've seen a couple that have them but I believe the "loop out" portion is on the transmitter side of the kit..
Make nice clean terminations and give it a shot with coupling the cats..  Your other option, if you really want to keep the server local to the LED is trying an HDMI 1 X 2 splitter at the LED, 1 output to the LED, the 2nd output to another HDMI extender, but I've never tried that and have no idea how that will work out for you.