Just arm waving here...
Excellent! I like it.
Does the epoxy cover the contacts? If so, could you now file a channel through the epoxy for each connection? Would that allow you to drop some liquid solder into the channel?
I've one of those solder irons that has a changable tip, held in by a side screw. Could you use a sewing needle for the tip? Use solder filings delivered by another needle?