Having read all 37 pages (!) of the thread this evening, here are a few observations. I didn't note all reply numbers.
A daughter of Major Alexander MacPherson married at "Trinity Chapel" in Ayr. A record says the clergyman was Episcopalian. The present Holy Trinity Episcopalian church which I understand dates from late 19thC., is in Fullarton Street, a short walk from Wellington Square. I don't know if it was built near the site of its' predecessor.
Death certificate of Catherine (page 32, reply 286). Her place of death was Royal Hospital, Chelsea. This supports her belonging to a military family as the organisation was for veterans.
Page 36, reply 317 census return. Address was "Glengall _____ ____". I can't read rest of address or that of next household. I assume it was the name of the house. Glengall was place of death on a death registration posted earlier in the thread. Can't remember who.
Reply 324 William MacPherson's death registration in Belfast posted yesterday at 21.03. This was already posted earlier in the thread, followed by a post + a photo of St. Oran where he died.
This may have been mentioned.
"Records of the Ayrshire Militia 1802-1883" by Hew Hamilton-Dalrymple & Tom Barclay. E-book. Can be borrowed/downloaded from South Ayrshire Library Service with a library membership. Hew Hamilton-Dalrymple was Earl of Stair.
Another book which mentioned an Alexander MacPherson was cited. It had Robert Burns in the title. Burns intended to emigrate to the West Indies but changed his mind when his book of poems was successful.