Batteries:
4S I suspect is too high a voltage at 14.8v. Not sure if the 3S would work the radio in particular as it gives the voltage as 11.1.
I also need one that fits the glider - no point in having one that is going to break lose. So far as I can see that make at least don't do one - the Yuasa . Since they are mounted behind my head (as they are in lots of gliders) they *must* be secure. The most common size in gliders (judging by our battery room) is the NP7-12 - 151mm x 65mm x 97.5mm - larger in one way and smaller in another than the ones in your URL. (Height isn't the key dimension in mine, width and depth are)
Unofficial installation:
Go read the chap who has given chapter and verse on it, just after your own post. You want to prove that we can carry a transponder that you will be able to detect, but driving a coach and horses through the regulations isn't a very bright thing to suggest IMHO, however stupid the regulations seem to be.
Transponder:
Mode C is all you need and they are cheap enough on US Ebay.
Maybe I struck unlucky, the only one there today is a CESSNA ARC RT-459A (Item no. 150105633270) and sorry but there is absolutely no way that could be fitted in my panel, even if it is completely reworked. The panel is about the width of a normal keyboard and half as high again, and is full. (ASI, altimeter, mechanical vario, electric vario, radio, T&S)
I *think* there is room on top of the coaming for Flarm & PCAS next door to each other (and I'll be measuring it next time I'm at the club). At least mine has a flat top to the coaming, a lot of gliders have a curved top.
Flarm and PCAS will not be illegal in any way, you will be able to detect me (so long as you can bear to part with £500 for Flarm and I have mine turned on), I will be able to detect you (so long as you are transponding).