Hello Yvonne -- you mentioned having "no luck finding any records for St. Mary's" (Eastry).
Perhaps I am misunderstanding what you meant here but these records do exist, and in a variety of places and sources. For example, in England, the Bishop's Transcripts (BTs) -- a contemporary copy of the PRs -- are at the Canterbury Cathedral Library with copies at the Kent Archives Office, the Kent FHS and the Society of Genealogists in London.
However, if you're not in England, both the PRs and the BTs can be searched on microfilm at any FHC, if you have one near you.
The LDS website at http://www.familysearch.org
lists -- in the Family History Library Catalog (FHLC) under Place Search -- the following records for Eastry during the time period you're interested in:
Bishop's transcripts, 1564-1898
Parish registers for Eastry, 1559-1951
Parish registers, 1559-1986
The microfilms for records of St. John Thanet (Margate) can similarly be found in the FHLC.
The confusion over surnames in the IGI is not surprising. The IGI, while invaluable in many ways, is notorious for errors, omissions, gaps and all manner of incorrect info. Therefore, not a source to rely on completely. Much better to go to the original documents.
Hope this is helpful. Regards, Andrea (admin for Kent Board)