re: How can I make splayed side for a round tray?

It would be easy(ish) on a bandsaw. Do you have one?
I would assemble the circle with maybe six scarfed together pieces and then just cut it on the bandsaw. As you can’t get the bandsaw blade into the middle of the circle, you would have to dry assemble, mark, cut the individual pieces, and then glue it up.
Short answer: Yes, you are biting off a mouthful but it can be done. Mike’s way will work too, this is just another option.