So based on nassau73's post above, I tried out the new mic plug in some other device inputs, and other plugs in my battery box input (as fanofjam just recommended).
It seems that my battery box input is very slightly wider than standard (based on my other devices), while the new mic plug is very slightly narrower than other mini-plugs I have. So basically my battery box would fit fine with any other plug I have, and the new mic plug would fit fine in any other device I have. It's just when the two are used together that the differences are additive and lead to the connection being loose enough to possible cause a problem.
It's a frustrating mismatch, but I wouldn't have the expertise to try to redo the mic plug, and I assume if I replaced the battery box with the same model (SP-SPSB-1) that it would have the same issue, as it is still very new. I suppose I could look for a 9v battery box made by another manufacturer - if anyone has a recommendation for that, please let me know. I have ordered the adaptor nulldogmas linked above. While I agree with jefflester that it adds another connection which could potentially cause a problem, the right angle plug should at least make the plug easier to firmly insert and to use with a rubber band, and for $4 it is certainly worth a try.
If anyone has any additional thoughts or recommendations, please let me know!