How do I install electrical through "new work" stucco?
It sounds like your problem is stucco depth (1 in or more) versus drywall depth (1/2 in or 5/8 in).

Can you find a mud ring/box extender that's appropriately gasketed for use in a wet environment? If so, you can use that to bulk up the box depth.

You could also look for a deeper box. That one looks like a pancake.

Or, since you mounted the box on plywood anyway, just use several pieces of plywood to push the base of the box out to an appropriate depth.