The first, and most important step IMO, is that you are asking the question. Secondly by doing so, no matter what choice(s) you make, you will be educated on how the numbers work and where you stack up in the safe, or not so safe, category. Once you know the facts it may eat on you as it did me (and I know others) and precipitate a change.
Based on calculations your 3/4 ton is going to be overloaded with that trailer. Short trips, "carry no water" etc. don't really mean anything. If you don't own the trailer you have to calculate and the only safe way to do that is using the gvw of the trailer and the percentage mentioned previously to stay somewhere close to being safe. Having extra cushion weightwise is a good thing, overloaded isn't.
Lengths of RVs don't predicate their weight. The layouts, appliances etc. all have a hand in it and as you've found, a "shorter" trailer can weigh more than a longer one. That's why you look to the weights.
You have a 2021 F250 diesel; what does that payload sticker say?? Maybe 2500lbs. or so? As was pointed out earlier the "guesstimated" load could easily run well over 4k - not good. In reality a 16,500 trailer should have a dually under it. I know lots of folks pull all kinds of trailers, and sizes, with a 3/4 ton truck. When they started putting the strong diesels into that size truck folks decided "it can pull it"...and it can. The underpinnings were built to carry the gvwr listed on the truck but the diesel makes folks think that that part is irrelevent....it's not.
In your situation if you want to keep the truck you need to be looking at a much lighter RV, or, get that dually.
Looking at a SRW 1 ton diesel isn't going to get you where you need to be with that much weight. Good luck in your search and decisions.