and I feel that symmetry can still be reasonably obtained with a rectangular arena.
I don't think so. Take a look at my (crude) examples. If you can think of a symmetrical rectangular shape, then draw it up (which I believe could only be done with 2 or 4 bots).The reason I am talking about perfect symmetry is to give the competitors each an EQUAL challenge. If you place, say, 5 competitors in the octagonal arena I drew up above(the left one), the game would be unbalanced since some of the bots would start closer together than the others.