I haven't actually listened to a episode of Ham Radio yet, so I don't really have any preference to Brett's style of recording other than the clips I've heard on the Challenge. However, if you've got a particular esthetic, go for it. If the joke works on the basic level, go for it. If it would work by adding on the complex layers that Brett likes, do that.
I really wanted to post just to offer a suggestion on how to try a recurring segment on a sketch podcast. I think Matt's idea of the Kids in the Hall style recurring segment, such as "Thirty Helens agree," or "It's a fact," is definitely approachable. The two thing those have in common, other than the visual aspect of looking the same (Helens in a field, girl running through a forest), is that they have a strong opening line that's repeated every time.
If you have some sketch you do that's say, a call-in-show, or a news segment, or some commentary or whatever, if you give it a strong opening line or music cue (or both) that can be repeated and gives the listener instant recognition, that might help you in this challenge.