I may be the only doing this but...

Water in a spray bottle and an old clothes iron set pretty high. Spray one side of the balsa, get it good and wet. Place wet side out wherever it's going and slowly start working at it with the iron occasionally spraying it down. It may not be the quickest, but I don't feel right about getting the wood wet on both sides and applying glue after. How much of the ca can the balsa suck in (capillary action) if the wood is already full of water?

My 0.02