Once a Holding card has been turned faceup, does it still count as filling the respective province and the province cannot be filled with another Dynasty card? Or can another dynasty card still be placed facedown on the province?

That being said, if all of a player's faceup Dynasty cards happen to be provinces, is the player stuck with them?

Yes, a holding takes up the province. Cards in provinces stay there until the end of each turn during the regroup phase, when you may discard any face up cards in your unbroken provinces, and must discard any face up cards in a broken province.

Thank you!

I've been having similar thoughts

Here's what I've been thinking could be a better idea