A possible middle ground is to do something with a primitive micrcontroller, where the architecture isn't terribly complicated but at least it requires learning about things like binary numbers and how numbers actually get passed from one piece of hardware to another. While they are much maligned, the 8 bit PIC chips are still available, and are extremely bare bones. I think there's a good reason why they were the favorite of hobbyists for a long time, before Arduino came along.

My college physics curriculum included building a 4 bit minicomputer from TTL (in the early 80s). While we were given the design, we still had to understand it in order to make it work, because nobody's machine ever came up on the first try.