Perhaps if you can two or three pilots to split the legs across, it may be a little easier to find pilots. One possible route might be:
(Phoenix) KDVT -> (KGNT) Grants-Milan Municipal -- 225 nm (Pilot based on Phoenix)
KGNT -> KSAF (Santa Fe) -> KLVS (Las Vegas NM) -- 139 nm (Pilot probably based in Santa Fe or Albequerque )
KLVS -> 00V (Meadow Lake) -- 200 nm (Pilot probably based on Colorado Springs/Denver)
So far, it is my experience that 200-300 nm (each way) is about as far as most pilots can go in a single day: at typical small plane cruising speeds, that can be 2-3 hours each way. Adding in an hour on each end to preflight the plane, meet and load the dogs, and meet and unload the dogs at the destination, and you suddenly have an 8-hour day or that distance.
As an example, I flew that exact route last spring, and the total flight (one way) was six hours in length, with one stop for fuel. While taxing, it was still more pleasant than driving ( 11h 45m according to Google maps ).
I might be able to assist on the last leg (to Colorado Springs/Denver) : but I'm currently trying to get a Great Dane from Dallas to Meadow Lake scheduled in conjunction with a Dallas pilot. Until that is resolved, I am unable to make any additional transport commitments.
Best of luck to you!
Currently grounded, no return to air date in sight.