My g/f hypothesized that my '97 has 235's because they didn't use 4x4 and it made it lower because she says it's hard to get in/out (which will be worse when I go to 31").
I'm surprised about 31" fitting in the carrier. But I took a look at mine and seems I have ab out 1.5" side clearance to the carrier, in the rear, none, but it could be more forward so long as it doesn't get too close to diff.
For a while I considered an aftermarket rear bumper with a tire carrier, which are cool, but then you have to open it to open the tailgate or use the step bumper to get in the bed. Also it puts weight further back which isn't good. On one hand I'd say for real serious off-road (where you could be in a situation where you had to use the spare, but you still need to be in 4x4), you do want the same size spare - if it (31") fits under the truck that would be fantastic. Shop manual says 225/65R15 is the max but I see space there. I could try a 31" once I get them and if it does fit, maybe I'd get a 5th tire. Might get 5th good wheel as well (the deep dish alloys). I guess one big advantage of the bumper-mount spare is if you have to get under the truck to get the spare you might be in mud etc. Plus you might have to put the flat in the carrier, which seems like technically according to Ford you wouldn't be able to do but maybe if it's flat you can.
My truck will look better with the 31" because it's a mild case of "shoes too small" appearance now. Plus I'll gain at least an inch in ground clearance which is really important, every inch counts there. Besides which the Coopers are pretty worn, I got about 5mm tread, it's not hard to fishtail the thing in the rain. 4.0L is gutsy. I made a lot of noise about it needing tires when I bought it, that helped in getting the price down (per advice TRS).
And not to forget it says in multiple places in the booklets and shop manuals, the size of tire is matched to the model of the truck and you should always use oem spec tire because that's how the truck was optimized.
Which I say of course with a grain of salt because if you have well thought out why am I going not-oem, and what are the effects, then sure, go to a non-oem-spec tire.
You had to lift your '98 but I should have zero issues on my '97 because 31" is how it came from the factory so the chance they won't fit is zero (in theory). It has 2" lift between the rear axle and the springs and it has the fender flares so it was set up for the bigger tire. Plus, the speedo reads significantly high vs gps so it should be close(r) to true speed with the correct tires.
I didn't have much fixing to do on the truck so really I haven't done much except used and shined it. The first thing I want to do is find the vents for the trans etc and run tubes up higher because the places I go 4x4 I'm in water a lot. Then I'd consider changing out the auto hubs. I really don't think the previous owners used 4x4 much if at all so they are probably fine, but here's the thing even Ford says these are not for your heavy duty off road, if you are doing that you should be using manual hubs. Past that I want front and rear hitches and a winch and then I think I'm good to go. With the right tires the truck has a lot of ground clearance, certainly as much or more than most stock pickups I see. I don't get the draw of big trucks for off road, seems to me you're better off with a smaller more maneuverable and lighter vehicle. In my limited off road experience what stood out to me is the common obstacle is rocks sticking up where you want to drive and worries about high centering, most likely on the differential, probably the back one. There's no solution to get higher up other than bigger tires and at 31" I'm at the limit of what would fit well without mods. Which I'm not ruling out, maybe later.