glue a second bottle cap, upside-down [edit: inverted from the first bottle cap], to the inside of the reservoir
That's a good idea, but not necessary. I drilled the hole in the bottle cap enough smaller than the ~1/8" wire that it holds quite firmly. I just about had to use a hammer to drive the wire through the cap, and the silicone sealant was not really necessary to seal it water tight.
I'm not sure what sort of glue would stick to the inside of that reservoir in any case. Maybe a second bottle cap underneath the first one (oriented the same direction) might prove effective, but there wouldn't be a lot of contact area for the glue to hold them together.
tanstaafl.