I use what used to be called a Lion miter trimmer. The picture shows how it looks, how it works is that the lever moves a set of extremely sharp cutters back and forth. You pre-cut the frame pieces to about 45 degrees and about 1/16th or so over size. The steel base has a stop for a small arm or mini fence. You slide your workpiece against the fence, then push maybe 1/32nd past the blade, then slide the blade across, trimming off a very tiny amount. This produces an exact 90 or 45 degree angle that is glass smooth. Theoretically you can cut other angles this way, but it is specific to picture frames, or making exact 90 rails and stiles. Mine is a Grizzly and has a couple of arms with a stop block to make sure lengths are exactly the same. This tool was originally made in the 1880s. My wife bought it for me to make frames for her paintings.
What you're makeing is going to require using something like a 22.5 degree router miter bit. You could also do this on a perfectly set up miter gauge, or my other alternative, which is a perfectly tuned Rockler table saw sled, which has a huge scale showing the exact angle in at least hundredths of a degree. But I had a lot of problems using thin kerf blades because the blad deflected just enough so I couldn't get a straight cut and ends wouldn't match up. Using a full kerf blade helped a lot.
Another method is to use the Wixey angle gauge to tilt a table saw blade to an exact angle, with a full kerf blade. See picture. I'd want to use a perfectly set miter gauge to hold those small parts, and a good sacrificial fence.
I would not use a miter saw or chop saw, just not accurate enough to suit me, even my Bosch saw isn't accurate enough for this precision work.
But for your project, the router bit approach would work well. Finally, even with all of that, sometimes a little cover up is required, and for that, Timber Mate filler has worked best for me. Takes stain and finish well and stays put even in the tiny amounts I actually use.
The more I do, the less I accomplish.