Do you have an Xbox One? Plug your OSSC into the HDMI In and plug your Xbox into your Elgato. It only has a frame of lag so for a lot of games it’s not a big deal and it works wonders! Just don’t use 5X on 240p games because it’ll cut off the top and bottom, but 960p works perfectly
EDIT: If you don’t have an Xbox One, I messed with it myself and I got it working at 960p. On OBS, set a custom resolution of 1280×960, and use the DirectShow version of the source, not the Elgato Game Capture HD source. It should have a (#01) at the end, or another number. If it blacks out, change USB port. Every so often if I use the Elgato directly, I have to plug it into another USB port and change it back to the DirectShow driver.