Does any modern Buddhist tradition use a Gregorian holiday schedule?
I've had a look around and I can't see actual Buddhist holidays that follow a Gregorian calendar. They all seem to shift around with lunar cycles. The Thai national calendar is a renumbered Gregorian calendar but the Buddhist festivals within that are lunar

However I practice with the Triratna Buddhist community in the UK and we have over a number of years celebrated 'Gregorian' festivals. For instance we have a lovely Buddhist ritual on winter solstice and then again on New Years Eve. I'm not sure if this quite answers your question and I appreciate that this isn't traditional or even standard but I think it's interesting that we are repurposing these days as Buddhist festivals just as Christians repurposed pagan festivals for Christmas and Easter.

So perhaps there are no Gregorian festivals (that I know of) right now but 'Western' Buddhist communities will be busily repurposing existing Gregorian festivals just like we are. Just a thought really.