Apologies for the (very) delayed response, and bombing email address on the 'Wyncolls of Suffolk & Essex' (WoS&E) site - long story involving dead computers, knacked hard drive(s), and lost uid & pw to update the material on the Freepages site.
Sadly I've no information about my g-g-grandfather Charles Wyncoll's wife Jane née Austen's family beyond what is in the WoS&E.
Col Charles Wyncoll (who wrote the book) refers to pedigrees in his possession for "Austens and Steddys", but sadly I've never been able to locate any archive of notes or unpublished material he may have had.
Hoping you may have had further luck elsewhere.
kind regards Charles -- email@example.com