Please understand that the quote you have provided has Jesus describing himself by using a metaphor ( a door ). There is nothing wrong with using this same metaphor for Mary, or at least a similar one, a gate. Just because a metaphor has been used once, doesn’t meet it is exclusive.
Jews would have keenly understood the metaphor of describing Mary as the arc of the new covenant, just like we understand what a gate is.
Describing Mary as the Holy of Holies just means that she is the most holy, since the original language had no superlative. It described the most holy place - the most inner room of the tabernacle. This is the same as her being addressed as blessed amogst women. Again an awkward translation from a language without superlatives. That is essential for understanding the meaning. These are just phrases used when the language has no superlative.
Speaking metaphorically of our lady as the Holy of Holies makes perfect sense. We could say that she is the new temple, or the new tabernacle,or the new holy of holies, it all means the same thing. It is a metaphor. She has replaced the man-made temple where God chose to live. The veil has been torn and God no longer lives in the temple. He chose to live in Mary. She is not only metaphorically, but literally the place where God resided. Understanding her as a new holy of holy room, like the temple inner room, is quite fitting indeed.
To further the analogy, maybe we could say that she is the new temple and her womb is the new inner room of the temple, the holy of holies.
As I learned at the tabernacle recreation though, these words have many meanings and can be used interchangeably.
Thank you OP. It is a wonderful thing to contemplate.