Can I attach SRAM trigger shifters to a 31.8mm braze on adapter? I noticed that Paul's Components make an adapter that enables SRAM shifters to be mounted to a road bar by exploiting the Matchmaker system. I live in England so anything from Paul's is très expensive, and I cant help but think... isn't it just an appropriately sized clamp with a screw thread? therefore can't any 31.8mm braze on adapter for front mechs be used in the same way?

My overall aim get a 10 speed shifter onto my bullhorn bars, and I have some time trial brakes already so cant use bar end shifters. The appearance is very important to me, I don't want anything that looks messy or completely bodged which is why I don't want to have multiple bar ends or anything.
The Matchmaker interface has a little bit more going on than that. As you can see in this illustration from the SRAM Shifter and Brake Lever User Manual, the mating surfaces of the mount and the shifter are profiled for a secure fit.

It is true that you could probably make something that does the same job. A braze on FD adaptor with a flatted section filed on doesn't strike me as putting the shifter far enough away from the bar, but that's just a guess.
If a little metalworking doesn't bother you and running a mountain shifter is what you want to do, just filing a normal 22.2 shifter mount so it clamps reasonably on your presumably 23.8 main bar diameter is also probably an option. Depending on what bullhorn you have, this may put the shifter in a more useful section of the bar.
My vote for best present-day way to do what you're after here is run it di2 with a climbing shifter only. You can pair it with any current di2 RD you want, mountain or road. Super clean, super functional.