Wonder what kind of load is on the battery with ignition power and fuel pump up. Consider this FI and its components require a bit more static juice then a carb with a mechanical fuel pump. Then add the starter load and you just might have a battery that is not up to the job.

I think that if you could graph the little battery you might find that the line would be heading south at a faster rate then a full size battery. There is a reason that the majority of the cars have the larger platform, it could just come down to the physics and in this case size just could be a factor.

You said it spins over faster jumped that could be telling you something. Ground to starter or bell housing got to agree I cannot think of a good reason that would matter.