Cheap, close, and short notice is a hard combo to achieve. I'm sure you also want a nice/decent place. You also mention wanting a place "<1 hr from 91". Don't know what "91" refers to. Do you mean Interstate 95? Coming from the midwest, would you not come down Int75? So I'm a little confused about which side of Orlando you are coming in from so I'll cover both sides.
- Bill Frederick Park at Turkey Lake is a City of Orlando park that has campsites which is north of Universal Studios and the FL turnpike. Cheap, yes, small unlevel sites, yes. Worn out bathouses, yes (I stayed there one night a few years ago)
- Lake Louisa State Park in Clermont on Hwy 27 is a place I book for my night(s) before Fort Wilderness. $24 a night plus a $7 utility fee. My only complaint is that the comfort stations (which are nice) have no AC (I have a popup so use the CS a bunch).
- The KOA in Kissimmee is on Hwy 192 east of the Fort. It's a small KOA but we had a poster stay there maybe two years ago and liked it. It will probably cost more than other choices.
- Also in Clermont, Orlando RV Resort is a Thousand Trails property (it's a like a time share for campers but they also rent sites by the night).
- Near I95 and Port Canaveral is Jetty Park on the Atlantic Coast. It is literally on the Atlantic Ocean beach next to the cruise ship line channel. It's worth more than an overnight stay but you can use it as such.
- Lake Griffin State Park is up near Wildwood where the Turnpike pulls off Int75. Not stayed there but looked at it as an option.
The main thing is last minute availability will be the tough question. RV's and Trailers are now more popular than ever so campgrounds tend to book up early (cheap ones first). Also you would need to contact them before closing as most will leave you the gate code and a checkin packet with your site number if you prepay for the night (the office closes and staff goes home).
Finally, the Fort rolls over to "the next day" at 6am or so. If you were to come into Orlando at 4am, I would just head to the Fort, let the guard at the entrance know you're checking in later that day, and he would likely direct you to the overflow parking lot (for long rigs, hitched up combos, etc) and you could catch a few hours of sleep in the car (it's not a place to set up and no hookups).
Bama Ed
PS - doing the overnight thing at Walmarts, etc is discouraged in Central Florida because municipalities want their tax revenue from overnight paid stays in campgrounds. However, some of the Rest Stops along Florida Interstates advertise "Overnight Security" if you want to catch some ZZZ's. But no hookups of course.