Max current through solder tracks?
I honestly don't know the answer to your question but I can point you in one direction.

I see circuit boards in commercial equipment where the traces have to handle significant current.  What the manufacturers seem to do is to have a bead of solder down the middle of each high-current trace.  The solder is usually not the full width of the trace but covers most of it (anywhere from 50% to 80% of the trace width).

What this does is improve the heat dissipation of the copper trace.  It doesn't actually reduce the trace resistance very much - copper is a far better conductor than solder - but it gives both more surface area as well as more thermal mass.

As a production technique, it seems to work well.  I rarely see damaged or destroyed traces unless the whole board section is blown up (including exploded relays) because of catastrophic shorts at the load terminals.