July is HOT. And WET. It rains often (almost daily) and although it is usually short, it is humid afterward as the water gets evaporated. Then it's back to HOT.
I've spent some summers in South Carolina, but only ever been to Florida in winter before. The daily rain doesn't worry me - the kids don't mind being wet. I'm a little worried that it is so humid you just end up damp all day though!
Cabins are nice. A queen and short bunk beds (not adult length) in the back bedroom and a sleeper sofa. You didn't mention how many people are in your family and if they are kids (to fit in the bunk bed) or what. We found that we enjoyed putting all the kids in the back bedroom to go to sleep and Mom and Dad (me) could enjoy a little peace and quiet in the living room and then sleep on the sofa bed. You have one bathroom to work with but you can call and request extra towels which helps (we had our 3 kids with us).
We are a family of 7 - by the time of the trip, the kids will be 16, 13, 11, 9, and 6. The three younger ones often end up piled into bunk beds at home right now, even though one of them has a separate bed, so I think they'd be just fine with bunks in the cabin or in a trailer. A little less certain about the two older ones who have some typical teen sensibilities about privacy and whatnot, but with enough bribery I bet we can get them to sleep in the back bedroom.
I get if you want to try a trailer rental stay in a campsite. You won't have as much space as a cabin so I would suggest renting the biggest trailer you want to pay for. The plus for campsites/trailers is you get more of the Fort vibe IMO and we enjoy being outside and meeting our neighbors and walkers past our site (although we don't go to the Fort in summer.

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I've been pricing the deluxe XL category from Meacham, which are 30-36'. I do like the appeal of the campsite feel, and meandering through the campground that you don't quite get with the cabins, but with the 2 teens we might need that extra space instead.
You can cook/eat/save meal money either way although camper ovens are usually off limits because the vendor doesn't want newbies messing with the pilot light (which has 2 temps: hi/lo regardless what the dial says). In the cabins you have a convection microwave which allows some flexibility.
I'd probably avoid the oven anyway - it just feels wrong during the heat of summer to slave over a hot oven! But we would definitely do some meals in; breakfasts probably every day, make our own lunches/snacks, and probably a few dinners.
A Fort stay usually means more days NOT spent in parks for a monorail resort-hop day, a Disney Springs day, a Disney putt-putt day, and time to turn young folks loose to roam the Fort. I will say on hot days in a park it's so great to come back to a cabin with AC. A trailer has AC too though.
That is what is appealing to me - the idea of spending a few non-park days, and just enjoying the Fort itself and exploring other resorts and Disney Springs. Definitely need AC during July. A couple of my kids are also big Harry Potter fans, so they would want to spend a day at Universal; not sure if it makes sense to try trekking over there during our stay or if it is better to just do a separate trip. It is a decent drive (about 19-20 hours depending on how many breaks).
If the $200 difference you mention is in total, I would skew toward a cabin because it's July and you won't be outside much probably during the day because of the heat. If it was spring/fall, I would lean toward the site/trailer. If in a cabin, you need to get out to see campsites, decorations, and engage campers in conversations as you walk by. We like talking trucks, campers, decorations, modifications, and other places we camp.
I was surprised the difference was so low, and then I realized I was comparing a 7 day to a 10 day stay. So it would be a shorter stay as well.
As for booking now, unfortunately I have to wait another month to get the next batch of details out from the Girl Scout convention. If the details don't line up for my fam for 2023, I'll start planning a 2024 Fort trip but for a cooler time than July. Late May/early June is a good time for us as the kids get out of school and I think it is slightly better weather. Would love to go in January/February, but just can't get the kids out of school long enough to make it worthwhile.