Hi Kittenface, couple of things here....
Your weights are certainly within limits, so the minivan "should" tow the TT just fine. How it performs doing so is something you'll have to assess. I would go ahead and give it a try, but be ready for the fact that you may not like the way it tows and you could be looking for a stouter vehicle in the future. FWIW, full size RWD vans make some of the best tow vehicles if you like/need the room in a van format.
You say the minivan has a towing package, double check to be sure that includes an auxiliary transmission cooler, you should see a small radiator sitting in front of the main engine radiator with lines connected to the transmission. The transmission is the weak point on these FWD vans, so even with aux cooling, be sure to get a temperature gauge installed for the transmission.
Regarding the hitch, what you had installed is known as the hitch receiver. You don;t need to change that to use a weight distributing hitch, the WD hitch head installs in the receiver in place of regular ball mount. It does sound like you have tight ground clearance, but again, you'll have to drive it and see. If you do wind up upgrading the tow vehicle, you can keep the WD hitch setup and keep using it.
Fresh water is only part of the weight equation...if the propane and battery(ies) are on the tongue, they contribute a lot to increasing tongue weight. Also, floorplan and location of storage compartments, whether ahead of or behind the axles, have a big influence on handling. Loading a lot of weight ahead of the TT axles adds to tongue weight but makes for stable handling. Loading behind the TT axles gives you a nice light tongue weight but makes the TT unstable to tow.
Best thing you can do is load the van and TT like you plan to go camping and head to the scales and get some real weights. You might also weigh with full fresh water, it may not be as bad as you think.
A lot of how the van performs will depend on your local roads and where you plan to travel. Heading an hour up to the lake on the weekend is different from a marathin road trip out West to the national parks.