After some more research I found people suggesting Weld-On #16, an acrylic adhesive that will actually melt PLA. A little of this applied to the parts, they said, and you can solvent weld PLA just ...

and Loctite PL 300 foamboard construction adhesive. In addition, we've used DAP Alex Plus and Dynaflex 230 (both acrylic products) to attach cork roadbed to wood and foam surfaces. Homasote ...