You’re close.
Yes, scenes are the way to open up the amp parameters, esp. since you can interpolate (gradually) the changes with the cross fader.
It’s not 4 parts per project, it’s 4 parts per bank.
Notably, in a new project, every pattern is associated with the first part in its bank. That is, patterns A1-A16 are by default assigned to part 1 in bank A, patterns B1-B16 are by default assigned to part 1 in bank B, and so on. But bank A’s part 1 is separate from bank B’s part 1. Add this to the fact (that you already seem to understand) that machine and effect settings are associated with individual parts, and the capacity for variations within a single project unfurls.
Here’s a thread I started recently when I was thinking (I think) along the same lines as you:
Hope that helps (and that I haven’t misspoken, ha!).