Can you run more cat6? There are plenty of HDMI over cat6 adapters that work well over some fairly long distances.
There are also plenty of extended length HDMI cables that are 50+ feet if you can fish through the HDMI end. They get a bit expensive at that length because they are hybrid fiber optic but no noise concerns.
USB also has adapters to run over cat6. They are usually limited to USB2.0 but that should be plenty to plug a small hub in for mouse and keyboard.
Cisco c3850-12x48u is about $150 on eBay.
The main problem is the idle power consumption. About 150w with nothing plugged in.