Stephanie, the registers of the Abbey at Bath were transcribed in the 19th Century.
A quick look at them shows there were an awful lot of Chapmans so it could take a long while to sort them out; and some may defy attempts at separating them. They don't go back as far as your earliest Chapman (parish registers don't usually go back that far) but might help with some of the slightly later ones .
https://archive.org/details/registersofabbey27abbe
https://archive.org/stream/registersabbeyc00jewegoog#page/n13/mode/2up/search/Chapman
Do check the Chapman burial on 29 April 1584, which is the date you have for
https://www.wikitree.com/wiki/Chapman-11504 it was a Julyan, who I found was probably the wife of a Richard Chapman https://www.wikitree.com/wiki/Chapman-11961
Who in turn appears to be the brother of Peter and son of Thomas
http://www.historyofparliamentonline.org/volume/1509-1558/member/chapman-richard-1504-80
For this period a subscription may not in fact help much, unless the person left a will. Some of these may be on Ancestry; they have all the wills proven at Canterbury. (and a few proved elsewhere).However there are printed transcriptions of Medieval Somerset Wills available. I found them linked from this page https://www.familysearch.org/wiki/en/Somerset_Probate_Records
Searching these should help you a great deal in your search for sources
Try also looking at The visitations of the County searching for histories of the towns, municipal records. Journals issued by local history and antiquarian societies.(these secondary sources may lead you to primary ones like church memorial brasses or wills or records of land transactions.They may include some more detail about the people you are researching; . Check the National Archives Catalogue, the local archives catalogues. If people died holding land then there an inquisition post mortem may have been held. There are abstracts of some of these online http://www.medievalgenealogy.org.uk/sources/ipm.shtml
(basically search anywhere and everywhere but try to verify secondary sources with primary ones or at least transcriptions of primary records)
