As you know, i do this commercially and 4 years ago went thru the same issue.
we initially started by using two trucks, two trailers, two drivers and putting the rig together on site. It worked, but was painful for the other person who had to sit there while you mowed (if it was too far to go back). Plus 2 pickups is a combined 6mpg.
A big pickup (or a F550 class vehicle) plus a big gooseneck is still class A CDL territory and 60 to 70 grand and you're occasionally worried about weight and definitely brakes.
What we did was this. (see picture)
It's a OTR tractor, as short as we could find. (224" wheelbase), it has a sleeper because sleeper trucks are 10 grand cheaper than day cabs. (no, I don't really know why, more demand I suppose). 30 grand.
Plus we added another 100 gallon fuel tank with a pump, so we can refuel on the job. We got a 2 line hydraulics and matched it with hydraulic tail 48' trailer for another 30 grand or so. This is the kind of trailer you see at all the rental yards. It's a heavy trailer, it's only rated for 35 tons. (yeah, I know, cracks me up) and even has a winch up front but the hydraulic ramps are awesome. As you can see we can get BOTH tractors with mowers on the trailer. Little one does the edges, tight stuff, big one does the big stuff, NO ONE can offer that. One truck, 6.5mpg, $1/mile or so which is actually better numbers than two pickups. Plus both people are working.
Takes 4 chains to do the batwing with tractor. heavy equipment over 10,000lbs, 30feet long, check the rulebook.
I drive it under 5000 miles per year (HVUT) and it weighs out fully loaded in the 57,000lb range. I register it at 80,000 because it makes no real difference and no it's not cheap. It really only gets used May thru Sept, but I drive as far as 100 miles away occasionally. (bidding a job over 200 miles away probably be too expensive, but you never know).
It stops way better than any non-air brake vehicle (which I know you know), and it's pretty maneuverable for a 70' long vehicle (SBFA). You never worry about being overweight (total or axles), the sleeper carries a LOT of tools. You have air with you all the time. (tires, air tools, blowing out radiator, totally awesome. We've replaced a stumpjumper on a job site do that with a pickup)
BUT
It doesn't fit sometimes. I simply can't do some jobs (no place to park, road too busy, but they are usually small and I don't miss them and we're talking 2 or 3 jobs a year.). I park on the side of the road a lot and no one cares. I carry cones with me if the road is busier than I expect.
It pays for itself. (but it didn't the first year or two I admit that)
BUT
In your situation, I'd buy a long pintle hitch trailer with air brakes and put it behind your dump truck. Cheapest solution that will get you going without losing money. Trailers are cheap to register and insure and you already have the truck, air to the back and CDL Class A.
But you wanted to see what we did.
HTH, feel free to PM