MacTaggart and Taggart

As far as burials are concerned, the obvious first question is what denomination were your MacTaggarts? That can often affect where someone was buried. Donegore Church of Ireland would be the most likely graveyard for a non RC burial in the 1600s, but sometimes folk had family plots in other parishes.  Donegore Church of Ireland does not have any early burial records. They were all destroyed in the 1922 fire. The church was once part of Kilbride parish so the family might have been buried there.

Unlikely to be a gravestone for someone who died in the 1600s unless they were very wealthy. You will also struggle to find any land records for the period unless they were major landowners (ie thousands of acres or more).

Tithe applotment records for 1833 list 3 Taggart farms in Ballynoe townland. They were the only Taggarts in Donegore parish at that era. No MacTaggarts (but it is the same name as I am sure you know).  Going by the 1901 census those families were Presbyterian, which indicates Scottish origins. Most of the families in the Donegore area have the same origins.  I mention that because you have Thomas born 1565 and Andrew in 1595. Most of the Scots families in the Donegore area only arrived around 1610 onwards, so if your ancestors were also Presbyterian they were probably were born in Scotland, and arrived in Ireland c1610 onwards.