I agree with Lonshanks, you need to consider both Halliday and Holliday references.
The St Mungo grave marker MI below is an example of the interchangeable use of both spellings.
Your only indicator of a Dumfriesshire connection being your Annandale reference, here are the small number of matching families using Thomas as a forename in Annandale (i.e. valley of the river Annan).
It’s a long shot but if you can match any of your American research to Holliday forenames, placenames etc you might be able to strengthen that link back to Dumfriesshire.
MIs in Annandale listing a Thomas HOLLIDAY (HALLIDAY)
Source: DGFHS database
Location: Dornock Old Parish Churchyard, DFS
Reference: Gilchrist G. et al, "Memorials in Dornock Churchyard", (1960)
1.
John HOLLIDAY in Corsehill, who died 13 October 1823 age 43 Also Thomas, his son,
who died 13th December 1840 age 33 And David, his son, who died 10th August 1842 age 29 Also Jean CARRUTHERS, his wife, who died 25th March 1849 age 62
2.
Elizabeth MITCHELL, spouse to Thomas HOLLIDAY in Corsehill, who died November 8th 1793 age 43 Also David HOLLIDAY, their son, who died young Also Janet HOLLIDAY, his daughter, she died 20th March 1808 age 21 Also above Thomas HOLLIDAY, who died 12th April 1816 age 64
And Thomas HOLLIDAY, their son, who died 28th July 1816 age 34 Also Janet, their daughter, who died at Corsehill 13th October 1823 age 43
Location: Gretna Old Parish Graveyard, DFS
Reference: Gilchrist G. et al, "Memorials of Graitney Parish", (1965)
Here lyes Thomas HOLIDAY in Mosband, who died March 26th 1746, of age 67 years
Location: Old Kirkconnel Churchyard, Middlebie Parish, DFS
Reference: Gilchrist G. et al, "Memorials in Old Kirkconnel Churchyard ", (1960)
James HALLIDAY, who died Brydekirk 16th Aug 1850 aged 84 Jannet SCOTT his spouse, who died there 5th March 1837 aged 70
Thomas their eldest son, who died Blackwoodridge 4th Sept 1816 age 27 Also two of their children who died young Agnes BELL, late wife of William HALLIDAY in Upper Mains of Brydekirk, 6th June 1873 aged 55 James their eldest son, who died Brydekirk 26th June 1875 aged 24 Above William HALLIDAY in Upper Mains of Brydekirk 3rd June 1879 aged 75
Location: St Mungo's Churchyard, by Nutholm, DFS
Reference: Gilchrist G. et al, "Memorials of St Mungo Parish", (1966)
Thomas HOLLIDAY, who died at Mirehead 1st December 1804 age 77 years
Also Margaret PORTEOUS, his spouse, who died November 11th 1819 age 73 years
Also John and Walter, their children
Also Sir Andrew HOLLIDAY, who died 6th September 1839 age 58 years, M.D.
Also of their grandson, James YOUNG And Jean, his daughter, who died at Mainshill 22nd March 1834 age 4 years Also Thomas HALLIDAY, Assistant Staff Surgeon, his son, who died at Jamaica February 1844 age 27 years
Also Janet, his daughter, who died at Lockerbie 31st October 1851 age 24 years
William HALLIDAY, who died in 1831 age 84 years Also Jannet RAE, his spouse, who died 1826 age 63 years Mary HALLIDAY, their daughter, who died 1800 age 10 years
Erected by Thomas HALLIDAY, their son, and grandson of James HALLIDAY, Farmer in Castlemilk Town Natives of this Parish
Cheers,
Sy