I have now made a new pair from a kit supplied by Concertina Spares. Here are the parts and tools laid out ready to start:
The thing that looks like a cheap Chinese wood chisel is actually a home-made leather edge-creasing tool.
The quality of the materials supplied in the kit were pretty good, though I was a little surprised at having to pay an extra £1.50 for the instructions (which were supplied as a PDF file on a CD).
One oddity regarding the instructions is that they seem to disagree with themselves about what type of glue to use. The page titled, "Tools and materials not in the kit," lists both PVA glue and impact adhesive. In fact you only need one type of glue and each has advantages and disadvantages. Most of the instructions tell you to use PVA and the procedure is based around PVA (i.e. apply it to one surface and then clamp the joint together until it dries), but in a couple of places they instead state that impact adhesive is a better choice because it produces a softer strap. If impact is the better choice, why not describe the process for using it instead? My own research suggested that a brand of impact adhesive called "barge cement" is the best (strongest) glue you can get for leather, so that is what I used.
The main drawback I found with barge cement (other than its high cost), as with all types of impact adhesive I've used, is that when the two parts touch it sticks together instantly and immovably, so if you don't get the joint perfectly aligned first time you're stuffed. I also found it difficult to remove excess dried glue. It worked well enough though, and I'm pleased with the end result and confident that it's not likely to come unstuck. If I was to make another set I would be tempted to experiment with hide or rabbit glue instead, because I have read that if you work the leather once the glue has dried it breaks up into lots of microscopic crystals and the joint becomes very flexible without significantly compromising its strength.
Here's one of the finished straps:
They look pretty nice and are infinitely more comfortable to use. The screws in the photo are incorrect (the heads are too large) - that's something I'll rectify when I make the new wooden ends. My attempts at decorative edge-creasing weren't very effective unfortunately, probably because the leather is so thin it isn't able to compress much at all.
Time spent making the new thumb straps: about 2-3 hours, though it took longer by the clock because the gluing was done in about five steps, which meant 20 minutes doing something else while the glue dried between each step.
 It took me a while to work out that the reason my hands hurt after five minutes' playing was mainly because the thumb straps fit so badly I was carrying most of the weight of the instrument on my little fingers instead.
 Apply a thin even coat to both surfaces of the joint, wait for it to dry, assemble carefully (bearing in mind you only get one chance to get it lined up correctly) and then beat the joint fairly hard with a mallet. Clamping is not needed.