So here is what I did. I just rolled up my sleeves and got to work.

I took the edges/points on the rim and slid them away from the boolean hole.  Then I welded the points that looked like they would be good tris or quads.  And I deleted a few edges.  I added a few to make good tris.  Then when I got the flat face of the rim to connect to the boolean hole, I was able to finally select the rim edge and bevel.

Didn't take too long.  Now it is clean without render abberition.