Hello KS,
I have flown routes similar to this (usually from PUB or COS going to PRC) on multiple occasions in aircraft varying from a C-150 to a DA-42 in the April/May timeframe. I'm going to assume that you are flying this in your L360.
First off Mark brings up some valid points. There are days where your route will not be doable due to IMC or severe turbulence (I'm going to ignore the DA issue as it's the L360, but for anyone else reading this, it's a very serious concern in smaller aircraft). If that happens the only route option would be down to LVS and then over (with consideration to my next point). Even this would have risk in mountain wave style turbulence.
Second is divert options, you can easily end up 50-100 miles from a suitable divert airport, your route actually does very well in this area. gavink42's route gets a bit far from airports for my liking between TAS and GUP and so does rgrazian's between FTI and around SJN.
So with that said here is what I think about your route and how I would change it:
I personally would avoid the MOAs that you penetrate during the route. This is a personal preference however.
Your route through the hayden pass is ok, I've never personally flown through that one, but it's well with the capability of your aircraft. My only concern with it is that you will need 12000' MSL to get a bare bones minimum 1000' ft clearance. And to be honest, I like more then that in case of downdrafts (which I have delt with in this area). I'd like 2000 ft clearance min, which brings you to 13000' ft. That's the hypoxia danger zone (even if legal).
I have the same issue with the wolf creek pass.
So with that in mind here is my route.
http://skyvector.com/?ll=33.77960391893 ... :A.K2.KCRQ
I ignore the last portion past the PHX area, but I would dog leg around the MOAs in west AZ.
I bring you down through the la veta pass as you can do it without breaking 10000', I wouldn't do it that low, but you could. That's the only mountain exposure in the entire route. The remainder of the dog legs are generally to keep you around other airports.
My route is longer by over 100NM, but lowers the required altitude down to 10000-11000 feet for a short portion of time (under 20 minutes) as opposed to 12-13k for a longer period (you'd be skirting the 12,500 feet for 30 minute rule, and while yes you can argue the "1 minute below then back up" part of that rule, that's a great way to pass out).
In terms of fuel stops, be careful of uncontrolled airports in this area unless all you want is fuel. I imagine after 650NM you will want food. Most of the airports that you fly over don't have a way to get off the airport for food (and no food on airport). Make sure you do your research on this.
Along my route "safe fuel stops" are SAF, AEG/ABQ, PAN (get some pie), and the PHX area (don't go to PHX).
Let me know if you have any questions.