Long-term, having one authenticator per battle.net account is not really that big of a deal. $32.50 (assuming the price has not changed) plus a little shipping, every "x" years is not much of an additional cost for a boxer.

Then you glue your authenticator to a piece of wood/rigid cardboard and label or color code them. And can log in, essentially as quickly as you can push your five authenticator buttons and swap your windows.

Or just put up with an artificial 2.5 minute extra delay, to log them all in from the same battle.net account, one after the other.