Thanks for the information, John. I'm unaware of any issues with Ren'Py with UHD graphics, but here's an idea that might help you:
When running the game, press Fn-F3 to bring up the video information. It'll look something like this:
Note the line near the bottom that says gl. That's the renderer my system is using. When you've pressed Fn-F3, make a note of yours. It's likely going to be either gl or gl2. What we're now going to do is change your renderer. What I want you to do now is press Shift-G. Up in the upper left portion of the screen that opens, you'll see the renderer settings. By default, Ren'Py is set to automatically choose:
Don't worry, any change we make here can easily be undone and won't affect any of your other Ren'Py games. What I want you do do is to click on the Force renderer text button that is opposite to what Ren'Py has chosen automatically for you. So if you saw 'gl', click on Force GL2 Renderer. Likewise, if it was 'gl2', click on Force GL Renderer.
After this, you'll need to Quit and restart the game. Let me know whether this fixes the issue for you.
Cheers!