"Needing some opinions on using the F250 with a 30' flat bed for Hot Shot"
The DOT is but a small concern in the big picture.
Coming from big rigs to a light duty pickup you are in for a maintenance cost surprise. Don't care if you have a Cumapart, Ford, Duramax, or an old forgotten IDI diesel. It's not the cost when, not if, you blow the engine, but, the rest of the truck that will eat your lunch in repairs. Front ends, transmissions, anything on the engine accessory belt... Some get lucky and get more miles than others out of an engine. Sometimes things go wrong and take your engine out like a bad oil filter, blown radiator, or hose. Fuel costs are not that much lower loaded and you are limited by weight. For Hot Shot loads fuel costs vs. a commercial HD truck on LTL isn't a big deal.
Figure a 250K life out of the Pickup. Some get more some less. Can you get your purchase cost money back out of the truck in 250K with the other expenses? Some argue the odds one engine lasts longer than another - this is something you can't bank on as once the warranty is up repairs come out of your pocket. We can talk about repair costs of a IDI 6.5TD that went 170K vs. the 3 times my 5.9 has been out of the truck in 120K. Yes, the re-redesigned IDI 6.5 is still in production for Military HUMVEE. Again sometimes it's just luck that matters more than how long an engine could last. A real factor is how much mechanical work you do on your truck and how much you have to hire out. Maybe the pay as a mechanic is better...
The Dual rear wheel truck allows more tongue weight or load in the bed plus trailer. Rumor has it that DRW gives you more stability.
You are dealing with LT tires, basically warmed over passenger car tires. The LT tires are rated from 3195 lbs single each to a max of ~4000 lbs for some rare ones. These are NOT the 19.5 or 22.5 commercial tires you are used to that normally can carry from 4000 lbs to past 4500 each. LT's don't have the load carrying capacity and they don't have long life - figure 30-45K tops from a set of 4 tires. (Add $400 more for 6 tires DRW that go the same short miles as the 4 SRW tires.) That is if they don't blow out or separate from the load. That said other than short life we have had decent luck with SRW LT tires. Just from short tire life alone I would suggest a 19.5 conversion for cost savings on the long haul.
From the door sticker on a dully you can super single it out as it has the higher GRAWR and GVWR numbers. The SRW 2500/3500 pickups are limited to a GVWR and GRAWR by tire capacity as they are the same tires used on the dual rear wheel trucks. So even with 19.5's on a SRW truck the door sticker limits your weight in the two ways.
SRW pickups are NOT "Super Single" versions of a DRW pickup! A DRW truck can carry ~4000 lbs where a SRW pickup 3500 is a little over 2000 lbs limited by the tires. 1993 or 2003 with SRW is about the same cargo capacity. (My 1993 has higher rated 16" tires than the 17" on my 2003 Dodge! The door stickers come out to about the same cargo weight. )
DOT stops anyone they feel like. Take the distance from a major city that would require logbooks and figure the DOT is stopping any 2500/3500 pickups with trailers to see if they are from that city, running commercial, and if they have a logbook. DOT doesn't care if you are DRW or SRW. If you are overloaded on either you are leaving the load behind, out of service for a day or more, and get to pay for the privilege. Overloaded on license plates or the rig's numbers itself is something I don't have the answer to as we never were caught over the weight rating of the vehicle.

Passed many DOT checks/checkpoints with SRW and even got a $50 check from the broker for passing. Hint NEVER pull into a rest area...
Ant the end of the day you need your CPM and fixed costs to bid jobs profitably and to see if this pays better than what you are doing now. Many people wind up broke with a worn out, used to be nice, pickup.
A good resource if you haven't seen it already is:
http://www.ooida.com/