That's disappointing, I've always got better performance out of even modest 7.4V lipos than 8.4V NiMh, but reality is reality.
That Lipo you're running is 600mAh (i.e. 0.6Ah) and 20/40C which means that it can notionally deliver 12W sustained and 24W peak. I'd want more for an AEG, and I'd also expect to go through at
least two of those during a full auto day, maybe three and into the fourth if you get a lot of play in. This is why dummy PEQ boxes and rewiring to the front are fairly popular.
Of course, there's always the possibility that it's just a duff battery. One of the few actually worthwhile posts I've seen on Facebook was a chap demonstrating that the internal cell resistance on airsoft batteries was far higher than it should be, and higher than cells sold for RC use. I strongly suspect that we get the bad cells, since our power requirements aren't as high as RC.
HobbyKing let you search by dimensions, if that's any help to you:
https://hobbyking.com/en_us/batteries-chargers/batteries/lipo.html
You'll want to filter by "Number of cells" first, i.e. 2, then you can start looking for skinny sticks.
I agree with going to Deans: if you only solder one thing on your gun, it should be that. Mini-Tamiya does work, but it's not great, and airsoft mini-Tamiya polarity is reversed compared to typical RC which limits choice.