I don't suppose there's any way in the world, short of a full frame and suspension transplant, that would allow the use of either of the later front suspensions? I see both of them use rack n pinion. I'd be willing to do the work if it was do-able.
I'm amazed Ford designed such an abortion and that people continued to buy them for so many years.
Care to elaborate? I'm only aware of one later suspension design that being SLA used in the 98+ Rangers. Easiest way to get it is buying a newer ranger, though I realize that for you this isn't the ideal/desired option it had to be said. There's only two ways to put this under an earlier Ranger. First is section the frame and add in the front clip, which will pretty much require tearing apart the entire front end of the truck. Second depends on your truck, if your 93 is an extended cab it is possible to swap the frame, it'll be a little more disassembly/reassembly work than a clip swap, but wouldn't require cutting and welding the frame. In short it is doable but will require quite a bit of work and down time for the truck either way it's done.
I definitely wouldn't call TIB/TTB and abortion. It was a very tough, very reliable suspension design that did for well for many years. When properly set-up and used it can also perform pretty well. I had an 84 2wd that was mostly a street truck and did daily driver duties for years. I did feel some of what you are describing, but not near as bad as you describe.
My first question is what kind of condition is the suspension in? (IE: Bushings, Ball Joints, Tie Rods)
Second have you checked your cab mounts?
Finally what does the truck have for sway bars?
First thing I'd look at is making sure that the suspension is up to par. If anything is loose up there it could cause the tires to wander which will magnify small irregularities in the road. I know that the shop probably checked your ball joints and tie rods last time you took the truck in for an alignment, but it can't hurt to double check. (unfortunately I can't recall the procedure for checking the on the TIB) I'd also check your wheel bearings, to do this jack up the beam on that side. Once the tire is off the ground try to shake the tire, and feel for any play, I'm pretty sure you'll notice it if their is any. I'd check the radius arm bushings, the best way I've heard of checking this is literally try to move the beam forward and aft with tire off the ground. I've heard of people being able to move the axle enough that it leaves a gap between the forward radius arm bushing and the bracket. The axle pivot bushing can also wear out causing problems, but I don't really know how you can check that one. There's got to be a way I just don't know it. If you find anything that's worn replace it, this'll tighten up the suspension and make the TIB work the way it should.
Then I'd look at the cab mounts, both the bushings and the frame mount points. The rubber can rot out and deteriorate which will allow the cab to rock more than it should, once again magnifying smaller surface irregularities in the road. These trucks are also bad about having a cab mounts on the frame rotting out. If the cab isn't solidly connected to the frame it's just as bad or worse than a rotted out bushing.
Finally I'd look into sway bars. I'm sure your truck came from the factory with a small front sway bar, most did by that time. My 84 came without any sway bars. That's when it really liked to rock all over the place with any little bounce or wave in the road. I started out in the pick-n-pull looking for a front bar for mine (it has a different mount style than 89+ rangers) and couldn't find anything. Since I had to buy new anyway I went straight to the biggest aftermarket bar I could find which was 1 1/4 inches. That made a huge difference in the way the truck felt and handled, but that was nothing compared to when I added a 1" rear bar from a BII. That rear bar tied everything together and it went from a small boat on the ocean to riding on rails (exaggerating of course but that's about how it felt). If you do have a front sway bar I'd check the end links to make sure they are still intact and not loose, some are made of plastic and like to break. If it were me I'd hit a few local junk yards and get the biggest front sway bar I can find from a Ranger, BII, or Explorer. On the front anything after 89 should fit until it went to SLA suspension, just compare the end links and if they are the same it should work. For the rear you probably don't have one, and will probably get your greatest improvement from adding one. I believe that any rear bar from 83-current will fit. I think the largest rear bar the ever came from the factory is a 1 inch bar that can be found on some BIIs, it's what I had on the 84 to match the big front bar. I think you will want to keep the diameter of a rear bar smaller than the front bar or else it will become too tight and try to spin out on you a lot more. I don't know the details on matching sizes front to rear, just what worked for me.
FYI after the sway bars and a good set of shocks (don't remember the brand) the 84 rode better than my 99 SLA. Granted my 99 is a 4x4 with torsion bars, but between the bars being decranked and sagged, I constantly got compliments for how good and smooth the ride was compared to many other t-bar SLA trucks. Both my dad and I though that the 84 also rode almost as good as the 02 2wd (coil sprung) Ranger he had, and we both though it handled better. IIRC he had around 50K on it when he traded it for a 4wd. So IMO a TIB can be made to ride and handle pretty nice.