Yeah, your cable tops out at HDMI 1.4 and can't handle the significantly higher data throughput rates that 60 fps 4K requires. I just checked with Monoprice and actually "chatted" with one of their reps. They have no HDMI 2.0 cables and won't for several months at a minimum.
I'm surprised that you had trouble pulling a single wire through a 2.5" conduit, especially with sweep 90s. There's cable lube to help smooth out the frictional resistance. It's a f'in mess to deal with, but it makes a dramatic difference when pulling through conduit. A helper on the other end feeding slack into the pipe also helps.
I guess we'll have to see what little trinkets they come out with during this transition to avoid the downgrading handshake issue.
VERY jealous of your projector, by the way!!!