The other thing that I have been meaning to try for years is optically clear casting resin. Here are some examples:
Polyurethane Casting Resins | Dalchem
Easycast Clear Resin
There are also equivalent epoxies:
Solid Solutions - Casting Resins
These products are used for potting electronics, making castings, and filling behind glass for some specific applications. As with acrylic resins, they can suffer from air bubbles rising up through them if you have not wet the substrate they are poured into and over.
All told, these will be expensive ways to get the clear fill, but once you have worked out the way to use them, they will be bullet proof. If you decide to try any of them I'd like to see your results. I've used these for casting and electronics, but not on timber.