Gooseneck difference?
A do it yourself will likely result in a very heavy tt.
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For arguments’ sake, let’s say you have 3k in payload left. That will hold a gooseneck of 12k (25%) to 15k (20%). If you can find a triple axle or a trailer with axles closer to the front of the trailer, you’ll take some of the tongue weight away.
For example, look at your typical RV trailer:
Here’s a quick pull, from the internet, just for example.

See how far forward the axles are? They carry more of the weight in the trailer, relieving tongue weight. However, the typical flatbed used to haul things like a tiny house are set up with axles further back.
No plug for Big Tex, but they have a good website, shows trailer sizes including weights and payload.

Finding flatbeds with axles much further forward than these, even in triples, is hard to find. They are designed for the truck to hold a lot of the weight.
Since you say you're 'looking at', I assume you don't own that F-250 yet? See if the dealer/seller will let you run it through a set of scales. That would be the best approach. With that, you'll know the weight of the truck (WoT).
Then, you have:
GVWR - WoT = available payload for hitch weight. (AP)
GCWR - WoT = available towing capacity for trailer weight. (ATC)
And, ideally, you want that hitch weight to be between 20-25% of the trailer weight. So take the lesser of AP x 4 and ATC. That'll be closer to your true trailer capacity. It's going to a lot lower than the towing guide states and will probably be a bit of shock.
Here's a worst case example using the numbers in the towing guide itself:
It says a F-250 4x4 CC has a max towing capacity of 14,400 lbs, and a GCWR of 23,500. Subtracting those numbers, gives us an assumed WoT of 9,100 lbs. At 10,000 GVWR, that's only 900 lbs of payload capacity. At a 25% pin weight, that's only a 3,600 lbs fiver it can tow, even though the guide says 14,400 lbs.
Here's a best case example:
F-250 4x2 RegCab - max tow 16,700 and GCWR of 23,500. Subtract those, assumed WoT of 6,800 lbs. at 10,000 lbs GVWR, that's 3,200 lbs payload. At 20% pin, that's 16,000 lbs fiver. Which, you see, is still less than the max tow that's listed, though not as far off as that worst case scenario.
Getting back to your needs, you'll need to get the true weight of the truck you're looking at in order to get your true specs. And then you'll have to be able to built your tiny home within those specs to be within spec.
Based on what I've seen on those Tiny Home shows on HGTV, most of those aren't going to be within spec of an F-250, but that doesn't mean it can't be done, as long as you're aware of your specs and willing to make some concessions to be within those specs.











