In case anyone wants to know. After trying various things to solve the screen blackout issue including signal boosters, high end HDMI cords, HDMI doctor, and lots of headaches we figured out the issue and fixed it!
Turns out that it was not an HDMI handshake issue! It was because we had the projector keystone set to auto correct. That, combined with the fact that this is in the basement and occasionally people are walking around upstairs, meant that whenever the projector shook, even if undetectable by our eyes, the keystone autocorrection kicked in, blacked the screen out for a few seconds while it adjusted, and brought back the picture! We turned the auto correction off and it hasn't happened once since then!
We also have a bunch more stuff down there now like a wet bar, fridge, and dim-able LEDs under the bar!