pleasedSo: this is a job for stick-soldering! meaning, heat the thing up to soldering temp then apply solder to the seam- it'll melt and flow into the spaces, just like one wants it to. It might be less likely to solder the damn binding wire into the mix, too.
For my second experimental piece, I'm going to bind everything together and then stick-solder it; the stick-soldering worked great for the gaps that were left on my previous attempt.
