Thinking through two hub cities.....
12 teams per hub = 3 games/day and teams would play every other day (no back to backs) in round robin.
Play-in best of 3: 8 teams involved; two games/day, teams play every other day.
Play offs, round 1, best of 7: 8 teams, 4 series. Two games/day, teams play every other day.
Play offs, round 2, best of 7: 4 teams, 2 series. One game/day, teams play every other day. (Or you could alternate hubs by day)
Rounds 3 & 4 - combine down to one hub.
Play offs, round 3, best of 7: 4 teams, 2 series. One game/day, teams play every other day. (And teams would not have to change/move locker rooms)
Play offs, round 4, best of 7: 2 teams, 1 series. One game every other day.
So: Hub 1/2. Divisions A-D. Schedule might be something like:
Hub 1:
(Day 1) Division A: RR game 1 - 12 noon local. RR game 2 - 4pm local. RR game 3 8pm local
(Games typically take 2.5 hours, plus .5 hour for warm up. 4 hours between games would give more time for ice to settle and sanitize benches, etc. Might need to sanitize stuff between periods as well. And there would be 2+ hours to sanitize locker rooms between games 1 and 3. Teams might not be able to get into locker room until 2 hours before game 3.)
Hub 2 would have similar schedule for Division C.
Day 2 would be divisions B and D. Etc.
Ideally, you have Hub 1 and Hub 2 staggered about 2 hours apart.
Down to two (or less) games/day at hub means no extra sanitizing the locker room during the day as there are two sets of locker rooms.