Hi Jerry,
There are a number of sources for R&P kits to install in TR3. There are several things to consider.
Before anything else (except checking tire pressure) I'd suggest you have the alignment checked. They might spot some problems that are causing heavier-than-usual steering. One cause might be binding in the trunnion. This could be due to a lack of lubrication (it's not easy to get grease in there - many use 90W gear oil instead, but that means using a special type of gun) and/or incorrect caster (possibly due to bumping a curb) or other things that cause binding in the steering (which can lead to damage).
A TR3's steering does require more effort than a modern car, especially at low speeds, but without actually test driving your car, it's hard to say if it's just normal or harder than normal. You'll have to be the judge of that and an alignment shop might be able to help.
Previous post at the link Geo provided mentions RevingtonTR's kit, which is probably the best method overall, but means permanent modifications to car's the frame. Still, this would be the most secure way to install a conversion like this.
The other kit from Bristish Auto Restorations sounds the same as TR Bitz in England, and probably others, a bolt-in that makes possible returning the car to stock, should that ever be necessary. (Also hang onto steering column parts that need replaced to work with R&P, too).
I've not installed any of these, but think most use a TR7 R&P unit, adapted for use (TR4-6 R&P are all too wide). I'm pretty sure installing thses will all also require modification of the steering column, possibly the switches and horn wiring as well.
When installing one of these kits, I'm sure they are pretty strict as to locating the rack. This is important because positioning it a little too high or low, forward or backward can begin to introduce some poor steering characteristics, such as bump steer. However, I would be confident kits offered by the more knowledgeable vendors address this and give good instructions how to set it up. Still, it might be something to ask the seller about, before buying.
Some say converting to R&P in a TR3 makes the car's steering a little over-sensitive, but it is something that can quickly be gotten used to. One reason for this is that TR3 have 0 degree castor in the front suspension. Shortly after it's introduction with R&P, TR4 front suspension geometry was changed to 3 degrees castor. This helps the front wheels self-center and reduces steering sensitivity to small bumps, ridges and unevenness in the road.
So, a possible additional enhancement may be to change to later TR4 (after approx. CT6400) front suspension parts. That would involve changing the vertical links/trunnions, upper and lower a-arms, and the ball joints. The upper fulcrum (upper/inner a-arm pivot) might need to be reversed to work right.
Note: All TR4 use the same as TR3's fixed inner/lower attachment for a-arms. TR4A and later cars don't, because it's adjustable, but isn't as strong as the earlier setup. The TR4A outer/lower a-arm setup might be better, though and uses a different vertical link/trunnion.
In fact, the next consideration is camber, which is non-adjustable from the factory on TR3/4. There are adjustable upper fulcrums available from Revington TR. The original camber was set at +2 to +3 degrees, good for the bias ply tires of the day. However, nearly all tires today are radials and they work better with 0 to -1 degree camber. Using steel-belted radial tires with the old style camber setup is another reason your steering feels heavy.
With these steering geometry modifications, to accomodate modern tires, it is possible the TR3 steering box will be more acceptable. However, you noted a lot of play due to wear in the mechanism, that needs to be addressed. One solution is a top cover with a spring built-in, that keeps the peg in the worm better, reduces play. These specially modified top covers are available from Revington and others, and look nearly stock.
BTW, Roger William's "How to Improve Triumph TR2 through TR4A" devotes part of a chapter and a few illustrations to installing R&P on the earlier cars. Being British, most of the sources Roger recommends are located in England, though.
Cheers!
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