Based on accounts of various ancient writers, scholars have painted a sketchy picture of the activities of an all-female cult that, perhaps as early as the sixth century B.C, worshipped a goddess known in latin as Bona Dea, "the good goddess."
A) Based on accounts of various ancient writers
scholars are not based on accounts, the picture is
B) Basing it on various ancient writers' accounts
"it" has no logical referent... better yet, "it" does not clearly refer to picture..
C) With accounts of various ancient writers used for a basis
a basis , is incorrect... used as a basis is better.
D) By the accounts of various ancient writers they used
this seems wrong..but cant really explain it...but if you compare it to E, D is verbose
E) Using accounts of various ancient writers
E should be the correct answer. No ambiguity. the clause starting with "using" correctly modifies scholars