I would suggest instead of door skins you go looking at 1/4" luan. The quality varies tremendously with different stores and chains. Home Depot and 84 Lumber having the best that I have found around here. No voids, excellent glue, thicker outer skins, and the cheapest prices. $8 a sheet at Home Depot.

Btw, this luan is being used as a barn wall and visibility screen on my farm and has gone through over half a year now exposed to all sorts of wet weather without any delamination. Some day I may actually paint the stuff.