So, I dont know that all of this is by any means a deal killer. Move your equipment on a trailer with a 2500/3500 and min trailer; do your material hauling with the 25,999 dump truck. Another option, maybe not ideal, is single cab 2wd dually, and a 16000 lbs dump trailer.
What I don't see is the curb weight on this dump trailer. I'm guessing 6k? That leaves you able to haul 10k of equipment or material. That is frankly, still more then the original F350 dump you wanted.
I do think your eventually end game will end up with a pick up moving equipment, and a 25999 dump truck; but in the short term...
Attached is a truck in Tex; F450, diesel, Class 2 truck, with the Kaufman trailer, you not lacking any of your initial wants. Note; it's a stake side, not a dump. and I don't know how they kept a diesel F450 crew cab under 10k lbs
Incase it isn't appearent; my thought process changed mid post as I worked my Google Foo.