Our present group does fairly well, intuitive cards are used, people have dice ready. One Player consistently has problems with AoO and such, while another is distracted often (whether its tending to a baby, sleeping, or trying to get a load of laundry done). The other two know the game and the rules, the GM is fluid and patient.
Not sure about your time table, seems to take you a bit longer to get through fights then us, but I understand.
Suggestions- cut table talk during combat, suggest the people look up their spells (know the area, range, etc), use intuitive cards, use a stop watch (“a round is six seconds, you can not see the entire combat, make your choice and stick to it. You have one minute when I turn your card”), and suggest that each Player figure out what they are going to do before their card is pulled (“Allen you are right after Dave, so be ready. Dave- your time starts now”).
(Oh, with the one-minute time table per person, cut that by five seconds per week until things seem more fluid, then slowly stop using it without alerting the Players. Should they start taking to long with their rounds again then start using the watch.)
When we played Champions at a library we had such a large group that our GM would start the combat, Players would take their turn and go to the store and back before their next turn would come up. It was terrible.
Best of luck, hope to hear that things are going better soon.