Lol! Actually, termux-storage-get seems only recently added to the Termux API. It’s in the package, but not in the documentation.
I had the idea to have a file picker for both the raw file and the hald-clut, and then a text dialog to enter a name for the output, but I can’t get it to work. It seems that each action launched by the termux-api runs as a separate background process, but not like a typical shell background process. The wait command doesn’t work with them, so they all run at once, not sequentially. 