I honestly don't think GMU matters much at all, with a very few exceptions where elk need to migrate in and the hunting is better in the late rifle seasons (mind you, if you want a big bull some of these are really good early, not many elk often means big elk) I'm personally confident that I can roll into almost anywhere and get a good encounter in a couple of days.
What strikes me is saying you aren't seeing much sign, if that is the case move until you do, I will not give a spot more than a single morning or evening hunt if it's not full of fresh sign, even two or three-day old sign isn't useful, elk might not be back for weeks... I think you are on the right track with the amount of mileage you are covering, but that's a long walk without seeing elk, let alone fresh sign, I'd be looking at a different elevation, aspect, or terrain type if I walked that far without fresh sign...
Also, spiking out can be super useful, but it also handcuffs you to an area, I'd usually rather do more walking and have the easy option to move if the action doesn't stay hot, that said, get up as early as you need to to be where you want to be by daylight, walking in the light just burns valuable hunting time.
as far as calling, in CO these days less is usually more, I'm pretty hesitant to call if I don't hear elk first, sure, sometimes you still get in a bugle fest on OTC public, when that happens for sure be ready to scream your head off, but endless cold calling doesn't often work well.
I think going deep is completely overrated, go where people aren't, most of the time in CO these days deep is the place most of the competition is, it's really easy to put the roadless filter on onX and call it E scouting, think about areas that are hard to access and hunt, plenty of them are right off a road.
one thing I didn't see mentioned was glassing, I'm always willing to burn time in a new area getting to where I can see, preferably around prime time, a well thought out glassing session can allow you to cover a huge amount of area and locate multiple herds to chase, I very rarely go into an area blind, I'll figure out how to glass it if at all possible first, same as fresh sign if I don't see elk I don't go with few exceptions...