So what is this "balanced-ternary" thing?

Ternary, also called trinary, is numeric system with three values per digit, as opposed to binary, which has two values per digit (1 and 0). Usually ternary means the values are 0,1, and 2 (similar to other bases); in balanced ternary the values are -1, 0, and 1. It can also be thought of as equivalent to a tri-valued logic (true, false, and unknown), in the same way that binary is equivalent to boolean logic.

A couple of early Soviet computers used it, but it hasn't really been messed with since. Probably because logic gates are more complicated to construct.

Not to mention thinking about it causes even more "Oh god oh god my brain" moments than even binary. ;)

I wouldn't say they're on the verge of prototype. They've found a way to slow down photons on a chip, but they're not at a point where it's practical (it requires chip printing at a level of precision that they can just barely accomplish; slowing photons requires heating, which is far too slow to be usable for switching)

I agree that ternary is a dead end. But really, scratch-building a processor isn't really about practicality.