I built a 20' flatbed GN trailer for my father. The only difference in the plans between the two was related to the hitch itself; the frame was the same on both. Make sure the axles are where you'd want them to be before converting it, otherwise you'll be moving those too. This is going to make the trailer more nose heavy due to all the additional steel up front; make sure your truck is rated to handle the load at the pin. The trailer itself will be heavier overall so keep in mind it will reduce the amount of weight you can haul now by however much weight you add.
If I recall correctly, getting it inspected, titled, and registered was simple, but I imagine that also varies by state. I've modified a few trailers but never bothered updating anything to do with the title because it didn't affect the weight or design significantly. If I were to do so, it just needs to be updated by submitting the same form I use to register a new/used trailer but checking the "corrected title" box instead of the new registration box.
Also check that this project will be worth it compared to just buying/trading for what you're wanting. If your state is anything like Texas, it'll now be titled as a home build instead of a factory trailer so resale will be reduced. Take that into account as well.
Finally, $700 sounds cheap for material and labor. Have them show you the design and proof that it is sufficient for the load rating of the frame.
