I have an original Banjo wheel that came on my TR4 which was similar in
construction to your TR3 wheel I believe.
I didn't like that thin rim, so I decided to put a leather wrap on the
wheel to fatten it up a bit. I sourced the leather wrap from Pep boys.
It is real leather, not one of those cheesy vinyl ones.
The wrap fit the diameter of the wheel but it was too loose.
I then got some black grip tape from a sporting goods store and went
around the entire wheel twice, wrapping it very tightly. I then put the
leather wrap on that.
I ended up with a gorgeous (IMHO) wheel that felt great.
I did later switch to a smaller momo steering wheel, but I like the looks
of the original better.
Anyway, there's one more option for you.