One test. Once. Acknowledged to be so. One time only. And with a nice consolation prize. This is no psyche test.
Why not assume average damage per successful attack, then? That would certainly prevent an extra action in nearly every round of combat. It would also remove a variable, and if you subscribe to the theory that "variables = bad" that seems to be the norm on this thread, it would seem to be a no-brainer.
I propose that, if you can tell me why you do not want to switch to average damage (and I mean a clear, well-thought-out answer here), you will probably know why some people do not want to switch to cyclic initiative.
In my case, I started out using the cyclic init from 3.0, and discovered pretty quick that there were some unintended consequences with the attention span of my group.

I then went to per-round init, but counting down init from 30 seemed to make the problem worse. So I switched to d10. Now everything is going really, really well.
Is this a solution for all groups? No. Some groups -- many, I'd guess -- don't even have a problem that needs solving. OTOH, I wouldn't quit an otherwise enjoyable game because the DM decided to have Initiative rolled on a d12. Nor would I quit because or rolling each round. Nor would I quit because of cyclic init.
I would quit because I knew the DM was fudging die rolls, though.
To each his own.
RC