Looks like we may be able to be a little more specific about a potential origin in the Ballymurn district.
Griffith's Valuation for Wexford was published in 1853.
https://www.askaboutireland.ie/griffith-valuation/Looking in Griffith's, I see a James Peare listed in the townland of Ballysilla, directly adjacent to Kilmallock to the east, and to Ballymurn on the south.
https://www.townlands.ie/wexford/ballaghkeen-south/kilmallock/kilmallock/ballysilla/James' holding is no. 18b, a 10.s house, meaning it is a low value mud-walled thatched cottage with just a few rooms. A poor laborer's cottage. At this time there is no Peare in the Rosslare area.
Now, this is just circumstantial, but your John's eldest son was named James, which is consistent with John in turn being the son of James, given Irish naming conventions. And Ballysilla is clearly within the Ballymurn/Kilmallock subdistrict where there is a family origin tradition. So, this seems a plausible origin location for your John.
I still think it likely that your Peares are an offshoot of the gentry family of the same name and same general location. Hard to avoid that conclusion given the rarity of the name. The discovery of James in Ballysilla just pushes back the possible interconnection by a generation.