Sucks to hear that
My Skyline came with an optima red top, so I know you can make "north american sized" batteries fit (at least, that particular model), but you probably know this already since you tried your Jeep battery. I haven't seen the tiny Japanese batteries in person, but based on the pictures...yeah...they must not have much in the cold cranking amps department.
Where and what is the cheapest BEST battery i can buy this a.m.?
...don't forget the triangle:
Cost, Reliability, Performance
Choose two.
Good luck!