Continuing to think out loud...
I'm back to thinking that the original idea of soldering the battery terminals to use a remote battery just as backup may be best. It'll allow the ISS to continue to run on solar power the majority of the time, just using the battery as backup as originally intended, and most likely be somewhat safer than running wires outside hooked up to ac inside. It seems not much more work would be required than whatever soldering and splicing is going to be required anyway, especially if it was decided that battery backup along with the ac/dc power adapter was desired.
I'm not sure how hooking up the battery to the jack on the ISS would work, but unless someone can say that it wouldn't interfere with the normal operation of the solar panel and supercap, but it appears that it would, I would go with azcrisf's original idea.