I bought a sheet of Revolution Ply. It was flat and cut cleanly. The first use was for a cabinet back that I applied wheatgrass wallpaper to. It worked fine.
The skins on this plywood look heavily grained, but feel smooth. However after spraying the second piece with Advance, I found that the grain telegraphed through the paint and looked awful. So, not so good for paint.
For Shaker door panels, it would not be acceptable, even with the low price.
Other options:
1/4” MDF. Available locally only in quarter sheets, so efficient cutting patterns are not really feasible. At $12.00 per quarter, ($48.00 for a full sheet), not a bargain.
1/2” MDF is available in 97” x 47” for $51.00 per sheet and seems like a better deal. It involves an extra steep (reducing the outer perimeter of the door panels to fit 1/4” slots in the rails and stiles). Also, 48” fits in my van. The 49” width requires that the store cut the panels before I load the van—a pain in the butt.
3/16” primed MDF bead board costs $26.00 for a 4’ x 8’ sheet. I am OK with the appearance for the Shaker cabinets, but I will be selling the house in a few years and I wonder if that would make it more difficult to sell.
3/6” tempered hardboard is available for $28.00 for a full sheet. It takes paint well, but in my mind it is associated with cheap cabinets.
Adding the wallpaper to the Revolution ply brings the panel cost up to birch ply prices, but looks pretty rich to my eye. About the same amount of work. As painting the panels separately.
Right now, I am leaning towards the 1/2” thick MDF for door panels.