I think you're right on, there. I've heard of other aircraft using this circling approach for visibility reasons, usually, like you, for visibility reasons. I like your conventional "base" and "final" calls as well, despite their not being discrete entities. The call is to help people figure out where to look. If you told them the truth most would be confused anyway.

I still fly a conventional rectangular pattern, but I'm an ol' squarehead who pays $5 for haircuts ($1 per side). I fly downwind at the "conventional" distance, but when possible, do cut base and final pretty short.

When using the CTAF at my home field, I often give a geographical reference to my base/final position, too.... "turning base 1/2 out," "turning base over Fred Meyer," "Short final over Lowes'", etc.

Ron Wanttaja