Not a big deal to punch all that down. Just leave a row or two between any power and other wires and I've seen little insulated condoms that go over punch down pins that will provide reasonable safety for hot wires. I would consider going from the stock cable to crimped or soldered lugs then to a barrier strip right near the radio and control head, then barrier strip to punchdown using CAT5 or similar cable. Or you could just go barrier strip to barrier strip and your done. Using barrier strip would also allow a more appropriate cable or several types mixing coax where needed and shielded or unshielded where needed.
I've worked on jobs relocating huge satellite uplink dishes 3,000mi away where we had to draw our own schematics at the original site, cut all cables then reinstall everything at the new site where the control equipment was further away and I had to splice all cables. Hundreds of them, lots of coax, lots of control cables, some 50 pair. Anything can be done.
Here is a 50 pair cable with various power and signal on the same cable and using this type of connection strip is plenty safe for power.
Here are just a few of the re-used cables that I had to install and splice.
Here are some of the racks of junk I had to install, splice and wire up and the finished antenna that were all transferred from another site. If I can do all this in a month you should be able to splice a radio control head in a couple of hours.

Any radio cable will have data, power and ground even if it uses a CAT6 for the connection between. None are designed to use the way you want to use it. If you go that route you may find issues in the future with operations. If its that critical I'd just run a dash mount and run the antenna cable thru the conduit. Much cleaner at that point.