I dug through some books and journals that Google has digitized and found a tracing of a stone in Bangor Abbey for a William Stevnstone d. 1627. I've attached it below. The records came from John Stevenson a writer in the early 1900s and the Ulster Archaeology Journal. Here is John Stevenson in his book, Two Centuries of Life in Down, 1600-1800.
Stevenson describes a monument to the first Dean of Down under the Ulster Scots, Mester John Gibson, in the old church of Bangor. “Later, with opportunity to wander any day, or every day in the churchyard, I found many memorial stones of the early Scots. The great Lord Claneboye [James Hamilton] must have seen them many times…
“Most of these early 17th-century stones are heavy oblong slabs with lettering in relief. The statement of name, with description of the commemorated and date of death, begins at one corner of the stone, and is carried round the margin to finish at the starting point, the centre space being devoted to heraldry and doggerel, --pious, affectionate, or appreciative. A man drowned in 1629, certified by the marginal inscription to have been ‘a worthy Gentleman,’ William Stevnstone, --perhaps one of my own people, for they were of the Ards—is thus made to express his hope in a joyful resurrection: --
‘This Corps I left on Walter Shore,
My Soule now bathes in Flodes of Glor,
No Tempests tose no Deeps can droune,
No Death can Reave that purchased Crovne,
I died in Chryst with Chryst I rest.
Chryst was my Hope my Gaine,
My Bodie heir in Grave doth lye,
In Grave not to remaine.’"
The reference to Walter Shore could either be poetic for Ballywater or could mean that he drowned (as Stevenson reads into it).
The stone also says he was 27, died in 1627, and was married to "E.E."