Just reading through quickly but my suggestion would have actually been to do the exact opposite....an earlier BT. Bearing in mind we all have different experience here, so not wanting to cause confusion - you've had some lovely support already
but my DD at 26 months is not high sleep needs but a 13-13.5h day with a 1.5-2h nap, with daycare would see her deep deep into OT territory. For us a 10.5h night with a cranky WU is almost always overtiredness.
Just to give you an idea she is at daycare Mon- Weds and does:
WU 6.45
Nap 11.45/12 for around 1h-1h15, though will refuse at least once a week, more often twice
BT 6.30 if no nap, 7 if naps
At home she does:
WU 7ish
Nap 1/1.30 for 1h30 (capped) - allow an extra 15 mins if completely exhausted
BT 7pm
With the odd nap refusal day at home.......like today..........
Just another thing to consider if pushing nap and /or BT doesn't get you the results you're hoping for