Mark,
If you've got the right connectors, you might try your 12v in to the JBox rather than the pair of Walmart Li-ion in series and see if you have the same problems. That way you can see if the issue is with the Li-ion batteries or with the combo of the JBox and Sonosax. If it does turn out to be some oddity with Li-ion batteries in series, you could ditch those and get a pair of NiMH RC battery packs.
At any rate, as I said, feel free to send the JBox back for a full refund.
-Todd