"What seems to work for me is to apply a tiny bit of flux to the cell, then melt some solder onto my wire (I would use #28 gauge here)."
Why are you using copper wire to solder to solar cells?
Easily available is thin 1/4" wide copper, tin, tin-plated copper, and
silver strips in any length. They are used by professional solar panel makers
because they are MUCH EASIER to work with than wire.
Gauges vary, but 30 gauge is easily available.
Where to find? E-bay has them in lots of sizes. I found some very good
25' rolls in Hobby Lobby. Both copper and silver (usually in the stained
glass department).
Maybe a bit more expensive than wire, but still reasonable, and , as I have learned,
much easier to work with on solar cells. They do weigh a bit more than wire, but not much.
john
AD5YE