Well, I ruined this. The Mig Thinner penetrated the layers of paint and melted the foam core, warping everything. I thought this only happened with stronger solvents, I should have given everything a thick coat of primer instead of white glue :\ This was a waste of my precious time, it's really frustrating.
Stupid mistake! Look how warped it got as the core melted because of the oil wash. The top-left corner of the wall also warped..