Good day Elwyn,
Thank you for you kind reply and interest. Yes, you are absolutely right in that the family was Presbyterian - I should have made mention of that, and, actually the Captain McCullough, master of the Minerva was indeed David McCullough, as I have now recently confirmed. I have found another resource which was of great help and was able to find some additional information there. It seems this family were for several generations mariners and masters of their own vessels.
Source and highly recommended resource:
IED (Irish Emigration Database): http://www.dippam.ac.uk/ied
The Belfast Newsletter, Friday, 12 March, 1773
"For NEWCASTLE, PHILADELPHIA and BALTIMORE.
The fine Ship MINERVA, Burthen about 350 tons and
upwards, Captain David McCullough, Commander, (now in this
Port) will positively sail (Wind and Weather permitting) the
10th Day of April next for the Ports aforesaid. For Freight,
Passage, Redemption or Service, apply to David Gaussan,
Merchant, in Newry, the Captain at Mr Darby Kene's or Mr
James McCullough, who will give due Attention at said House,
and Mr Archibald Herrons, in Banbridge, every Monday; every
Wednesday at Mr Andrew Armurs in Rathfryland; and every
Saturday, at Mr McKey's, in Dromore. The Ship is very
compleat [complete?] for the Passenger Trade, being nearly
6 Feet high between Decks, the Captain a humane good Man,
well acquainted in the Trade, and carried out of this Port
last Season upwards of 423 Passengers, whom he landed safe,
and received the Applause of every Individual on board.
Proper care shall be taken to have the Ship well Victualled,
and with every Necessary to render the Passage comfortable
and agreeable as the Captain is determined to continue in
the Passenger Trade.
Newry 1st March, 1773.
N.B. Servants of all sorts will meet with the greatest
Encouregement [Encouragement?]; particularly Tradesmen by
applying above.
N.B. Three days after Arrival at Newcastle, any Persons
inclining to go to Baltimore may be offered that they shall
be Accomodated [Accommodated?] with Carriage for that
Purpose, they paying 6s 6d Sterl. [Sterling?] Addition to
common Passage."
In this newspaper advertisement is also mentioned as a contact his nephew James (then a young men and at some point the cabin boy) who was also shipwrecked with his uncle (off of Wales) during one of these voyages (unsure if this was with the Minerva or some other vessel).
The Belfast News-letter, Friday 25 February to Tuesday 1 March, 1774
"
For NEWCASTLE, PHILADELPHIA and BALTIMORE.
The fine Ship MINERVA, Burthen about 350 tons and
upwards, Captain David McCullough, Commander, (now in this
Port) will positively sail (Wind and Weather permitting) the
10th Day of April next for the Ports aforesaid. For Freight,
Passage, Redemption or Service, apply to David Gaussan,
Merchant, in Newry, the Captain at Mr Darby Kene's or Mr
James McCullough, who will give due Attention at said House,
and Mr Archibald Herrons, in Banbridge, every Monday; every
Wednesday at Mr Andrew Armurs in Rathfryland; and every
Saturday, at Mr McKey's, in Dromore. The Ship is very
compleat [complete?] for the Passenger Trade, being nearly
6 Feet high between Decks, the Captain a humane good Man,
well acquainted in the Trade, and carried out of this Port
last Season upwards of 423 Passengers, whom he landed safe,
and received the Applause of every Individual on board.
Proper care shall be taken to have the Ship well Victualled,
and with every Necessary to render the Passage comfortable
and agreeable as the Captain is determined to continue in
the Passenger Trade.
Newry 1st March, 1773.
N.B. Servants of all sorts will meet with the greatest
Encouregement [Encouragement?]; particularly Tradesmen by
applying above.
N.B. Three days after Arrival at Newcastle, any Persons
inclining to go to Baltimore may be offered that they shall
be Accomodated [Accommodated?] with Carriage for that
Purpose, they paying 6s 6d Sterl. [Sterling?] Addition to
common Passage."
In any case, my greatest thanks for the lead regarding this ship as it helped me uncover a wee bit more information...