Additionally some states have this thing called a CDL-B, which puts you in the class "A" for pulling heavy, but forbids you from pulling commercially. It's pretty much designed for those folks who have huge campers or race trailers that require medium- or heavy-duty tractors to move them, but who will be only pulling their own stuff with said tractors, and therefore do not need the commercial insurance rates. May wanna look into that for your state.
Also, by looking at how you have the trailers listed, I assume you're talking about a flat-deck gooseneck, and not say a horse trailer? Weight regulations aside (I do not know them well), your the factory GCVWR is IIRC around 17000 lbs, so considering your truck is already at about 7k you are indeed limited to a 10k trailer, but this is 10k of actual weight, not 10k trailer GVWR. Can you pull an 18k-rated trailer - sure you can, but trailer itself will be heavier than the 10k-rated one, which will leave you with less payload. Heck you can hook up to a 39k-rated trailer and pull it around, but if said trailer weighs 8k alone what's the point, you will only be able to load it up with 2k of cargo.