I went through a similar search in order to camp with two grandkids and a TT with our 2008 Explorer until we can afford a stronger TV.
We like the wolf pup BHS16. With an UWR of 3097#, GTWR of 3877#, factory assumed Tongue weight of 377# (haven't weighed that yet). CAT scale weight loaded for a 3 day camp on axle with WDH 3680#, without WDH 3600# (WDH pushes weight to steering axle and trailer axle).
IF you can find this size trailer with a double axle, get that. My TT axle is rated at 3500# so I went on a rampage removing all the things I can do without. With the above weights, I also was 20# from my TV drive axle GWR WITh the WDH. Without the WDH, I was 120# OVER the axle GWR. Only things in the TV for camping was me, SWMBO, our 90# lab. I have also cleaned out a LOT of stuff I routinely kept in the TV in my weight loss program.
SWMBO's only real complaint about the TT (AFTER I changed out the mattress) is the side to side sleeping master bed since whoever is in front has to crawl over the other for night time BR visits. I did NOT want a Murphy bed but for getting in and out of bed in this size TT, it does make some sense. We did not want to have to move or convert our bed every day.
Anyways, there are a LOT more weight limit considerations that you (& I) did not allow for. I strongly recommend you take your Explorer to a scale with what you expect to have in the TV while towing and everyone aboard. Add about 75# to your numbers on the rear axle for a WDH, then you will have an idea of what your remaining axle and payload capacities are. Seems a little over the top at first but after towing, I should have done this to start with.
And the scary part is the weighing was done on our third outing with the TT. First time we had a load of wood in the back of the Explorer, no kids, about 15 miles one way. 2nd time, no wood, one 145# grandson added, 70 miles one way, half interstates. We were way overloaded! 2nd and 3rd trips were camping with our daughter's family who have their own TT.