How concentrated can I brew iced tea?

The amount of tea you use won't affect the flavor of tea adversely; the way you brew it will. This also depends on what kind of tea you're making (black, oolong, green, white, herbal). Greater quantities of tannins are released in higher-temperature water, which makes the tea more bitter.

TL;DR: If you follow the instructions for brewing temperature and time, you should be able to more or less add as much tea as you want.

Black teas are brewed with boiling water, typically for 2-3 minutes. Green, white and oolong teas are usually brewed at lower temp (180 F) for 3-4 minutes, and herbal teas at just below boiling for anywhere from 4-8 minutes.

I've found that I can easily more than double the amount of tea leaves I use, brew it at the recommended temperature for the recommended time (most tea packages should have instructions), and store the 2x concentrated tea in my refrigerator. Upton Tea has a great guide to tea for water temps and amounts. They also have instructions for hot and cold brewing iced tea - they recommend double or tripling the leaf quantity when hot brewing, then diluting to taste. (I buy a lot of my teas from here, and their instructions have never steered me wrong.)

If you're looking for even more information about preparation of and descriptions / histories of different types of tea, I recommend the Harney & Sons Guide to Tea.

I usually use 10 "standard" teabags per final gallon of iced tea. Like you, I steep them in less hot water first (I'd estimate about 4-6 cups, too) then dilute to 1 gallon.

That amount seems to provide enough strength for me. Since the tea infuses well into that amount of water, I'd guess you could try your plan of keeping concentrated tea on hand...say 2x concentrated or so. Maybe you could do 4x.

In chemistry class a while ago, I remember there was some way of calculating how much of a particular substance could be dissolved in a given volume of solvent (like water). If you really wanted to know the maximum concentration of tea you could make, that's what you'd need to look up. It's also temperature and pressure dependent, so cold water will "hold" less tea than hot water.

This wikipedia article seemed to have some related chemistry info: http://en.wikipedia.org/wiki/Solubility

I use 6 family size luzianne tea bags per 12 cups water.

I brew in a 12 cup coffee maker minus a filter. The tea concentration is served 50% water / 50% tea and some ice. It never tastes diluted.

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.

This makes me think of the Tibetans who actually boil their tea to extract all their flavor to make yak butter tea. If you're using tea bags tea or broken leaves loose leaf tea then you can give it a try. If you're steeping some fine full leaf or bud rich teas, then it will for sure adversely affect the flavor.

Ideal tea-water-ratio: Tea isn't like coffee, in which brewing is approached in a kind of scientific way. The intensity of the brew is quite personal and depends a lot on the tea characteristics, such as tea type (oolong, black, green etc), tea form (crushed, powder, loose leaf, buds etc), and aged/non-aged etc. The best way to find out is simply by trial and error.