I'm super confused. Why wouldn't OP just put $20 of value on a regular MetroCard and not have to deal with buying a second card on the way back to JFK? That would cost only $19.05.
(Buy a MetroCard for $18.05 from the machine. With the 11% bonus the value will end up being $20.03. There is a $1 fee, so it ends up costing $19.05.)
This seems like the obvious way to go.