I meant to put this reply in this thread and it somehow ended up in the thread on how to fold paper liners lol. Dunno if it was me being spacey or what, but here goes.
I make reusable, cut-to-fit mold liners with the semi-translucent plastic shelf liner at home depot meant for lining wire shelving. I get the 18'' x 8' rolls for $7 and there's a smoother side to it which is the side that goes against the soap. It's in the wire shelving section.
Once the soap is properly hardened, there is no sticking, and it withstands gelling, cpop, and overheating just fine. Soap pops right out. If you try to take it out before all the way hard or have a soap that's just naturally sticky on bottom, just peel carefully and there's barely any, if at all,of sticking.
I make folded mold liners similar to how you would with paper, and use clear packing tape to secure the tops of the cut flaps at either end. Lift the liner out of the mold, undo the tape at the two edges, let the sides fall open and dump the soap right out!
Now the other side of this stuff has a slight texture to it, which might be enough for an adhesive to grab on to, to glue it into your mold. Silicone adhesive seems like it would work the best.
Why don't you just 'paint' the inside of your mold with silicone?