Two thoughts:
1) Here at the Ridgway Colorado Railroad Museum (www.ridgwayrailroadmuseum.org) we have used a special very thin epoxy to saturate dry rotted wood for strength in cosmetic restorations of 100 year old railcars. This stuff is like water and is made for working on wooden boats. I forget the name, but I know you can find similar products by googling - try something like wood restoration epoxy. I expect to use this stuff on old window sills in a historic building this summer.
2) My first job after graduate school was in a US Geological Survey rock analysis lab, and one of the things we did was prepare thin sections of rock. Without going into a lot of detail, one step was to glue a flat piece of rock to a glass microscope slide. Classically we used a material called Lakeside cement, which was very brittle and a PITA. Then a special epoxy came out with the optical properties we required, so we used that. To make it thin enough to seep into porous rocks like sandstones, we thinned it. If I remember (that was - ahem - 45 years ago), we used either xylene or alcohol (probably alcohol), and it worked fine. You might try this, because by varying the mixture, you can get the thickness you want.