So, you can obviously keep your tea at the 4-6 cup concentration by just not diluting it before storage, that is perhaps a reasonable amount to keep in a bottle in the fridge and should require no sacrifices. You might want to store it more concentrated in the future, but this will be easy, take very few changes, and you can get used to the process of re-diluting by hand on a per-cup basis. It will also be one less variable when you're trying various extra-concentrated brewed tea methods, if you're used to mixing from concentrate you can more easily tell if the problem with a batch is the brewing or if mixing differently will help.
You can also concentrate the (pre-prepared) tea extract by heating gently over time. As long as it isn't held at a higher temperature than you steeped it at, it shouldn't alter the flavor compounds much. I would suggest leaving it on the stove on low while you're cooking (and eating), or even putting it in the oven - it is low temp enough, and will take long enough, that you don't need to be hovering over it. Reducing the concentrate by any great volume will take a while, especially at lower temps, and it might change the flavors just a little - but probably it will change the tastes less than trying new, ultra-concentrated brewing methods.
As for brewing the tea to a more concentrated infusion in the first place, I'm not sure. You can obviously just try it, double the amount of tea next time and see how it goes, maybe one more addition of it works well (by which time you're down to a cup or two, so). But, there are two considerations - one is the rate of infusion of the tea into the water has to do with the relative concentration of the flavor compounds, so the compounds may extract more slowly with a higher concentration (which can make things tricky if brewing with a timer), and at some point will simply not extract fully, leaving good flavor in the tea leaves. You may have to leave the tea longer to get the same extraction, or you may throw out tea leaves with some life left in them. At some point, you may even run into physical issues - trying to brew a gallon's worth of tea leaves in a cup may be physically problematic, think of trying to fit a gallon's worth of tea, which would be at least 5tbs (16 "tea"spoons) of tea leaves, or 16 tea bags and more if you prefer it strong, into a single cup's worth of water - at some point there might actually not be enough liquid, or too much water might soak into the tea or teabags, or evaporate off while brewing, to actually keep the tea moving and brewing, or not settling out and burning, something like that.
The other thing is, it will make a difference how much flavor variation you are willing to tolerate - it is really hard to say how much change is too much, when it comes to flavor differences. Along the same lines, the kind of tea will also make a difference - but that goes back to flavor tolerances, I suppose. I suspect higher end teas will probably not come out as good on this sort of concentrated brewing method, or perhaps the kind of people who favor higher end teas will notice the difference more, since they seem to need very precise brewing methods, while tea bags are likely more forgiving.