Michael, thanks for taking a look. I was able to do a small chamfer on the whole object like you did.

I also tried another object that to my human eyes looks kind of similar.



And I can chamfer just the front edges.



I know that to my eyes the shapes look kind of similar, but they must be quite different mathematically. Are there any suggestions for what to avoid if you want to later chamfer something? "Stick with only straight edges" isn't it, because I've done lots of fillets on curves. "Only planar surfaces that join each other" isn't it either, because this model shows chamfers on curved surfaces and edges.