May be worth at least looking into contractors in another time zone to cover your overnight on-call. My team did this a couple years ago and it's significantly eased up our on-call rotation, at least to the point that we're only getting called for major outages while the offshore team handles the minor issues, change/release support and things that go bump in the night. There's still weeks where we put in significant time if there's a major issue, but we're not getting woken up for every little alert that goes off.

I should also add my team has an automatic comp day at the end of our rotation, though that's handled on a team-by-team basis. Plus it's not uncommon to get an extra comp day if you have a particularly brutal week or support some major off-hours work.