Hi,
It probably could be done, with some serious, careful work. I've not seen it done.
Another possible candidate would be a '71-'72 Pinto R&P unit. It's also pretty common and used in a wide variety of custom installations.
The biggest problem would be getting all the geometry just right. The length, movement and orientation of the tie rods needs to be pretty exact, or all sorts of strange things can happen. "Bump steer", for example. Steering problems can be downright dangerous.
But, I've not specifically heard of either of the Ford units being installed in any TR.
I've also never seen or heard of the later TR4 or TR4A/250/6 R&P units being retrofitted to TR3, either. I think the problem is both of these are too wide and will not work with the narrower track of the TR3.
The available TR3 R&P conversion kits are based on TR7 R&P unit. There are two varieties. One bolts right in (TR Bitz), easier to install and easier to return the car to original should that become important. The other needs to be welded in (Revington TR), a stronger setup but more of a job to install or remove.
Notice too that Triumph converted to 3 degrees of castor shortly after switching to R&P in the TR4. TR2/3 and very early TR4s have 0 castor, which is less than ideal for use with R&P, might make for pretty light and "squirrely" steering.
However, it would be a pretty easy job to swap later 3 degree upper/lower control arms and trunnion into a TR3 that's being converted to R&P. A bit of added work and expense, though. (If I were doing it, I'd try to make it an adjustable setup: TR4A or later, using shims on the lower control arms, or some sort of custom setup that adjusts the upper fulcrum mounting point).
Have you considered some of the "improved" TR3 steering boxes? I know there are several offered, less of a chore to install and a lot cheaper than the R&P conversion kits. British Frame & Engine sells one of the "improvements", I'm not sure of the details. Ken works closely with the British TR vendors who offer such things (Revington, Recestorations, TriumphTune) and might have some other suggestions. (britishframeandengine.com)
Cheers!
Alan