Here's how I did it.
I took one of the squeeze valves and removed the rubber check valve by cutting it out, then inserted two of the rings that come with the squeeze valves and pushed them to the bottom. Finally I sanded down one ring so that it was tapered on in the inside, just enough that the solid valve can fit in about 2mm.
The two rings in the bottom prevent the top ring from getting pushed down into the squeeze valve body. The top ring will protrude a little bit but it fits inside the SV housing with room to spare. It must be pushed down to fill, as that is how the SV works. I'm working on a simple wire clip that might eliminate that problem. I use the SV mouth piece with the SV as the squeeze valve setup isn't really held on that well, strictly for filling purposes.