I've picked up bookmatched 4' long pieces of veneer at Rockler for what I thought was a very affordable price. I've got a few cabinet tops to deal with, but that won't happen until my building is done and I've got a room dedicated to cabinet restoring.
There is no "salvaging" of what you've got - however since it's a Singer, the tops are sold quite often on eBay if you want to replace the whole top with something in much nicer shape instead of replacing veneer. A lot depends on your level of ability and interest.