wing tank fuel used first
Rainboe,
interesting theory of highly non-standard procedure to use wing tank fuel first, which brings you completely out of the certified envelope for the 738.
However - using this procedure will not lead to fuel starvation, because after the wing tanks are half empty the fuel in the center tank will automatically be drained into the main tank #1 (left wing tank), which gradually will lead to a nasty imbalance.
Therefore your proposed procedure does not make a lot of sense.
If it is really necessary to get cold fuel out of the wings (to avoid icing on ground) there is an approved procedure to transfer fuel from the wings INTO the center tank when you are on ground - so you are able to refuel the wing tanks with warm fuel.
The procedure takes a while, but you stay within approved area!