Hi
I wonder if daycare would try putting her down first or last out of the group so she can settle a bit more easily? I get that naptime is 1pm but they can't possibly put everyone down at the same time, so someone would go first ~12:30-12:40ish and so on til the last one is down at 1ish then the staff can take their lunches.
Would daycare consider giving her 2 naps? 2x30mins is better than 1x30mins...
Something that helped us was getting DS put into a quiet corner to read/sit/whatever before nap time so he could wind down rather than going straight from the chaos of lunchtime and cleanup to sleep which just turned out to be too hard for him.
It does sound a lot like some of this is 'just' that she misses you - lots of people find babies who previously slept through wake for nighttime snuggles when they go back to work and LO goes to daycare.
I would certainly stick with EBT for those days with no nap or only 30mins - you can even do super EBT at 5pm if she's ready to go down - she may well tack on and sleep 12-13hr, maybe even 14hr overnight at times.