Hi.

I liked your request.
I think it's a reasonable feature to want in the game.
I tried to make it, but there is a problem with Issac's API.
The game is made in such a way that it doesn't allow for this to be done by a mod.
I could actually get it working, but the problem is that the game is 'paused' not only while the pause menu is open but also when the character transitions from one room to another.

In simpler words, I did it, but it also stops the music for half a second every time you enter a new room.

There is another option, though...
If you are using Repentogon, the requested feature is very easy to achieve.
The problem with that is Repentogon does not support Rep+ still, and I am playing with that DLC, so I won't go the extra mile to implement it for that specific version of the game.

I will shortly upload the mod in its current state, but I don't think you are gonna like it with that half a second pause of the music on room change.

Here is the mod.