John,
Since you've clearly eliminated solder from contention, I would suggest:
http://www.allelectronics.com/make-a-store/item/WG-1/CONDUCTIVE-GLUE-0.3-FL.OZ.//1.html
"An all-purpose, electrically conductive glue ideal for bonding all kinds of
low-voltage connections. Makes a permanent bond without heat. Lead-free. 0.3
fl.oz. jar."
While it's really more of a conductive paint than a glue, it's been useful
to "replate" switch contacts on IR remote control units and to attach small,
fine wires like those required by glass solar panels where soldering may
cause serious damage if not done expertly. They also sell all sorts of
battery holders and soldering tools.
You might be able to gain strength by building up the material in layers and
then covering it with hot melt glue to add physical strength. Even will all
that I would solder but use a small alligator clip to "wick" the iron's heat
away from the plastic. Buy a new iron and some spare tips and practive a
little. I was amazed to learn how much a good tip is worth when soldering.