Andy Lincoln,in Dearborn MI
Jack,
See if your local lumberyard /plywood supplier has MDO in stock.
This is a paper-faced plywood that is used alot for highway/road signage.
It is made to withstand the outdoors,it is super smooth ready for painting.You may even find it pre-primed.It is available good 1 side or good 2 sides and in (atleast) 1/2" and 3/4" thicknesses.
I have no experience with Varathane in an outdoor application so I cannot comment on your finishing schedule.

Andy