I agree that DNA is going to be our only option.I did locate nearly all the E.C.A.'s.Footnote has uploaded about 61% of them so far.
NARA-M1104. "Eastern Cherokee Applications of the U.S. Court of Claims, 1906-1909"
Application numbers are:
#34208 Elizabeth Perry-Ham #34209 Cordelia Ham-Davis #34210 Richard Perry #34211 Edith Perry-Sheets #34212 Arthur Sheets #34213 Mary Sheets-Pennington #44579 Edith Clelland (this one isn't uploaded yet, but some loose papers were in Elizabeth Perry-Ham's file) #44701 or 44707 (can't read the last number, but it isn't uploaded yet anyway)
Apparently all these applications were rejected because Abigail Easterd-Vanover was not listed in the Eastern Cherokee Rolls.She might have been missed, might have used her Cherokee name and they couldn't find her under Easterd, or may not have actually been N.A.As you said, only the DNA will tell us for sure.