Martha's Vineyard had a large deaf population and a native sign language. I read that this had been partially reconstructed by looking at the differences between ASL and LSF, as modern ASL is basically LSF with a strong MVSL influence.
I don't know that there is an answer to this question. Part of the difficulty here is that ASL isn't just LSF with a strong MVSL influence. ASL is certainly a daughter language of LSF, and there is certainly MVSL influence there, but there is also a lot of the langauge influenced from home sign.
Reconstruction of MVSL to any extent would would be be very difficult. Simple substraction of LSF from ASL wouldn't work because you couldn't know if the result was from home sign or MVSL. It would theoretically be possible to perform a comparison between Old Kent Sign Language but there isn't any record of signs from OKSL. (Or for that matter hard evidence of it's existance.)
Without either more daughter langauges of MVSL, or insight into OKSL that we don't have, I doubt any real reconstruction is possible.