Back stay broke 3 weeks ago. 5" seas 10 -15 knots winds. Was lucky the whole rig didn't come down. To my sons quick thinking, drop sails, tighten topping lift and main sheets, snatch block, line, secure line to back stay and in snatch block then to wench... Motored on in about 12 miles. To make a long story short, replaced it all the next week. You should do the same...
As they say in golf, hockey, sailing, and indeed in life,
"Nice Save"!! And your son's a quick-thinker and even better, a quick actor.
Absent topping lift on a smaller vessel, the answer would be to keep the main up and hope the leech, with tension from the mainsheet, is strong enough to hold the mast up for a couple of minutes at least, while you try to use a halyard led aft to a deck fitting and winched tight to take the strain off the sailcloth.
To paraphrase "any landing you walk away from is a good landing",
"any stay failure where the mast ends up still vertical, is a good stay failure" ;-)