Overwind secondaries work just fine on unencapsulated toroidal transformers provided you use a heavy enough gauge of wire to carry the max. current without overheating the insulation under it.
Assuming the ripple can be treated as an assymetric triangle wave, 80mV ripple, AC coupled true RMS, is close to 280mV pk-pk. In practice its more likely to be bit less than that due to rounding of the troughs and peaks. If its quasi-sinusoidal it would be about 230mV pk-pk, so you need at least that much more headroom to have *ZERO* margin. That's within the gains you could expect from substituting a beefy Schottky rectifier bridge, but the overwind is a cheaper and better option, as you can adjust the head room more freely to get enough margin for low line full load operation.
One zero cost option would be to eliminate half of the diode drops in the bridge rectifier, using the classic two diode center tapped secondary full wave rectifier topology, by putting the secondaries in series, feeding the bridge from the ends, ignoring its negative terminal and taking its output between its positive terminal and the winding center tap. This could be compounded with the gains from the lower Vf of Schottky diodes by replacing the bridge with a beefy common cathode dual Schottky diode, winding ends to the anodes, + out from the cathode. That's got the potential to gain you up to a volt of extra headroom, without even looking fugly!
A suitable diode will be found feeding the +12V output of almost any scrap PC PSU. Don't forget it will need a silpad or similar and an insulating top hat washer on its mounting screw if its a non-isolated package as the tab will be the cathode.