The Fort will rent a tent and cot for a nightly fee. They will set it up and take it down before/after your arrival.
This brochures shows tent and cot costs. The site rate is for the group camping area unfortunately. Here is what you get for that:
What time of year are you considering visiting? Will you have a rental car? I know some sleeping bags can compress down pretty far.
For $70 a night you can get a rental popup trailer from one of the rental vendors. Travel trailers start around $100 per night but you get better rates the longer your rental is (up to a week). You just have to check websites and consider what you want.
You can do dining plan but the Fort has limited options so you would be going off to Wilderness Lodge or Contemporary nearby for meals sometimes. And companies like Garden Grocer or WeGoShop can deliver groceries if you don't have a rental car.