Have you looked at Jewish Gen? Even if your family is not Jewish, there is a lot of research about Bessarabia on that platform. Mostly free.
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In regards to researching family records in Wittenberg, Bessarabia, other than using Ancestry, FamilySearch, or perhaps Fold3, the only organization I could find is the Germans from Russia Heritage Society, which from your description it sounds like you have reached out to this organization already. If not please find their website link below:
We hope this information is helpful and best of luck with your research!