Extenders, port savers or any other extra connections are not recommended.
HDMI troubleshooting. Get your system in one place, usually in the case of a projector/TV you'll probably have to take it down and bring it close to your equipment. Test the system with short HDMI cable less than 2 meters (6 feet). If the system works and doesn't with your longer cables you have a cabling problem, period! Find a solution for it, either a different cable, HDMI signal restorer or a balun. Remove all port savers, wall plates, 90 degree adapters, etc. Each connection changes capacitance and may be the straw the breaks the camels back. A cable between devices is usually best.
If the system doesn't work with short cables then I'd look at an equipment problem either in the settings or a problem with the equipment. Although it is possible to have a bad short cable it is less likely. It might be a pain to take down the projector/ TV or move the other equipment but until you isolate the type of problem you are having you can spend a lot of time chasing your tale.
A quick test without moving equipment is to change the resolution of your equipment to 480P and see if you get a picture. If you do it is probably a cabling problem. If you don't it could still be the cable on the DDC line, so it doesn't rule it out. Putting all the equipment together and using short cables is the best diagnosing you can do without test equipment. This can't be stated enough.