I thought some more about not using initiative at all, as described in this post. Whether or not I decide to give in and dump d6-only weapons (probably won't,) I do think I've refined it even more.
(1) The side that attacks first announces actions first. If that side also surprised the other, they get to attack, then announce their next attack. If there's a tie (both sides charge, for example,) players get to choose whether to announce first or last. This order stays the same for the rest of the combat.
(2) Hasted actions all go first, then normal actions, then slowed.
(3) Actions are otherwise more or less simultaneous, even though one side announces first. If there is ever a question about interrupted actions, lowest damage goes first. If comparing damaging attacks to actions that don't do damage, roll a d6 for the action's pseudo-damage. If doing this for a spell, the pseudo-damage can't be higher than the spell's level.
There, sorted. Don't really have to bother with extra rolls or comparing Dex or anything else. I've dropped weapon length, although on a charge I would probably still resolve pole weapons first. Otherwise, all weapon length would do is allow a special action, "Move out of Reach". But that's worth a separate post.