Pro Tip Needed: How Do You Pull HDMI Cables?

I used RapidRun in the past and it worked quite well. The ends of the cables have a cap with a loop to assist in pulling the cable as well. I've used them to run around 50 feet from a central server in a back room to LFDs mounted on a showroom floor.

Have you thought about using RJ45 to HDMI converters like this one?

I've used the cheap two-wire HDMI-over-UTP extenders on several sites now with great success.

First time I used an HDMI extender though, was in a case where a client decided to add a remote monitor last minute, I only had one spare UTP anywhere near the area, and even that was a pain to fish to where it was needed. We went with a very expensive ($300+) high-end extender that also carried serial data and had full HDCP support... it worked fine with the system's onboard (Intel GPU) HDMI for a couple years, as well as with the DVI head on a loaner we put in when we sent the machine for warranty service, but after the machine came back with a new Radeon card installed (don't even get me started), it stopped working. As near as I was ever able to determine, the Radeon's HDCP wasn't getting along with the extenders, so while Windows would detect and add the display, it refused to send a picture.

Anyway... +1 for cheap, basic, two-UTP HDMI extenders; this specific unit has been flawless for me.

Anyone have any experience with Muxlab baluns?

Dont' pull HDMI at all. Run Cat6 and use HDMI over category baluns. You can run thin and cheap CAT6 and you will be able to run as long as you want. There are baluns out there that can run high speed HDMI, ethernet, ARC audio and IR over a single CAT6 over long distance. Also if you run 2 CAT6 in place of an HDMI and use the current offering of baluns you can swap them in the future with new baluns for whaterver is new without having to rip your walls apart.