Door of Destinies gets its charge counters off casts, so your Door will still charge up even if a sliver or two gets countered
Ah yes, worse Thrummingbird
That being said, if a card is only seeing play in Standard and Standard alone, then the Three Rs are pointless, and the card will probably drop when it leaves (but if that is the case, the card is probably not a great card)
However, if the permanent leaves play via a flicker effect, it retains no memory of its status and would return unflipped
If you're nostalgic for this era of Disney like I am, then you'll love this deck
Overall, while the concept of the card is interesting, it may not see much play in competitive Magic: The Gathering decks