As for tie-breakers, the mini-conversation of "what's your initiative mod and dex", "5 and 11" "3 and 16" is actually quicker than just about anything else you could do. The rare event where you would then incorporate the actual fiction might finally encompass about the same amount of time as rerolling, re-adding, and then going back to the original rolls in order to note the overall initiative order .... and draws deeper attention to the actual fiction, to boot.
Also, what John Magnum said.
When MC calls for initiative, everybody gets excited, reach for their dice, and start rolling .... When you hear "23", "17", and "19", followed by "4", that's just unnecessarily deflating, especially if everybody's modifiers are roughly the same. It's also a little jarring when I, as MC, am writing down initiative order and I see such a meaninglessly wide divergence. And by meaningless, I mean that, beyond simple ordering, there is no real qualitative or quantitative difference between a 23 and a 4. This isn't even a pass/fail type of thing -- it's nothing more than simple ordering. However, since magnitude and/or degree of success is important in so many other areas of the game, people automatically assign value or significance with such a disparity -- which, in the case of initiative, is fucking stupid.
When there are wildly varying initiative modifiers within the party, players already quite readily accept that the intra-party initiative order is pretty-much set -- and that's on a d20. And to be fair, they're statistically kinda justified.
So much for avoiding determinism.
In the interest of full disclosure, I probably should voice the fact that I do have a soft spot for the d12. It's visually pleasing, the finer granularity over the d10 is significant enough to note (making it an adequate replacement for the d20 for some things), .... and is the least loved die in the game (yes, that is a shameless appeal to pity).
