I think that my first piece of advice is to only cross the bridge when you have reached it. So I wouldn’t think seriously about buying a Bartok until you have heard the Network Bridge and are convinced that that is the way that you want to go.
As for the update question with your Matrix DAC as that is the only point that you do not like then the obvious and cheapest solution would be to buy a refurbished laptop PC just for this purpose. As you do not need anything flash then the lowest spec will do. Or, as such an update is not going to be a regular feature of your life, do you not have a friend who has a laptop that you can just borrow?
Secondly I do not recommend stacking components. Some audio racks are modular and allow additional levels to be added . Is that an option? Or could you simply change your rack ? Or add a small secondary rack?Given the price of a Bartok unless you are using e.g. an HRS rack then that may be a minor financial consideration.
As for a balanced system, yes that is broadly desirable. But as an old Naim hand I will revert to the original Naim and Linn philosophy. If you lose the Information at the front end you cannot replace it later in the system. So the source is the least appropriate place to save money or, conversely, it it the most appropriate place to spend the most money. As I remarked to the late Charles Hansen ( Ayre) ; the speakers make the most difference to the sound of the music, the source makes the most difference to the music itself. He liked that and asked my permission to use it. Sadly he passed away a few weeks later. In any case although I no longer have a single Naim component ( I sold my last piece, a NAT01/NAPST tuner, to a friend a couple of months ago) I am still an admirer of the brand and think that you need have no concern about matching your combination to a Bartok.
What a bugger having to wait in tomorrow for TNT. Actually i have always had a good experience with them. I hope that you may be working from home and not have to take time off.