Every time I see something mounted and not being used, or nothing on the mount, I wonder what kind of sensor can I hang on it? I like your idea of using something already there.
Rainwise makes something called a monomount which is a smaller dish mounting system with the correct sized insert so their MarkIII will slide onto the piece already inside the support.
Yours looks like one of the newer dishes with a 5 LNB dish, heavier duty and if I recall correctly, the size of the support pipe is bigger than the mounts for earlier dishes. And Rainwise doesn't sell just the insert for a dish mount that you may already have.
I've spent an hour in the plumbing section of our big box home improvement store looking for the correctly sized PVC pipe that they use to make snug fits, and with the limited stuff they carry (two aisles) vs. the different brands with Schedule 40 and regular and PVC vs. CPVC and so on, have failed to come up with the correct piece of pipe to do what I want. And without a lathe to turn down a bigger piece (who knows what that would do to the integrity of the material and who wants to loose an expensive station to a weak mount) I'm stuck doing what you have seen here where people use an overlap type of bracket to clamp high and low.
Speaking of mounting weaknesses.... In the picture of the dish you have attached, it appears that while this is the heavy duty mount with the two stabilizing arms, only the top two bolts of the big bracket are bolted to the fascia of the trim around the roof. That certainly can allow a lot of flexing. I'm glad some jobber didn't mount that for your dish antenna and think that it was OK. Really a crappy mounting job if it is what I think it is from the picture. Nonetheless, you don't have much wind load with the wx station, and should be able to pull the dish and slip most anything on there but don't depend upon the mount to stabilize you on the roof or ladder or we'll be hearing of your hospitalization.
Good luck. If you figure out something take some detailed pictures and post a 'here's how I done it' for us to learn from. If you find a piece of pipe to fit the mount, take notes on the type and let us know.
Dale