The reason not to use sugar water is that it's nutritionally deficient. It supplies energy, but nothing else. You can get around this by adding a tiny amount of boiled flour. It's not an ideal solution, but it works. Feeding yeast nothing but sucrose doesn't cause them to lose the ability to ferment other sugars; it just causes them to temporarily turn off the genes responsible for making maltase. They'll turn them back on as needed. This will cause a minor delay, not a total failure.
I would follow eastoak's recommendation of harvesting the cake from your 2 gallon brew. It's already increased its population size to the point you want, and the yeast is much fresher than the vial in your fridge. Unless your 2 Gal batch was an imperial stout and your next batch is a blonde, you can skip washing the yeast if it seems like too much trouble. What settled out once before will settle out again.