Doors and Windows - Sealing New Window

I put a new larger window in my bathroom. When I cut the opening I encountered 1/2" plywood sheathing, foil faced 1" rigid insulation, expanded steel lathe, 1" of stucco which I believe is painted but could be a finish coat of some sort. There was no house wrap or tar paper of any kind. Because all this equals about 2 1/4" thick I built a frame around the opening 1" thick to screw the window flange to. This keeps my window from being sunken in. Is this the best way to keep the window frame proud of the stucco? How do I best seal the frame I made and the window from water intrusion? Any suggestions on sealing the stucco around the window? Any help or suggestions would be appreciated.

No replies, not surprising. You have literally opened a can of worms.......and potential leaks. This is one that should be handled by a pro that understands EIFS stucco and windows, hard to find..