I think replacing those doors with stained wood doors would look better than painting based on that pic, but that would depend if the wood would tie in with the rest of the space after you remodel.

Do you need the doors since you mention bookshelves or do you mean the bookshelf doors like this ? This one could be an interesting way to handle that issue .

Another idea. Make the doors a feature, not so much this style but wanted to provide a feel from further back to see impact.

You just need higher quality doors that blend in and compliment the stone. OR I like the bookcase idea-hidden room-panic room etc.

I would not keep those Colonial 6 panel doors. They seem totally out of place.

Here are some alternatives.

Thank you all for your suggestions. We have cherry stairs on the other side of the room and we have a beam that we are thinking to also wrap with cherry. They are medium toned cherry, not dark at all. And we definitely do not want the existing style for the doors. So we'll go with some more modern looking doors.
For the bookcase idea, we are not sure how these hidden doors will look on the other side, in the bedroom.

Replace them with more modern doors (flat panel shaker) painted black.