Alex'r and John Caldwell are both mentioned on page 39 (under TIRCREEVAN) of a "brilliant...packed with information on a dozen townlands in Magilligan" Manuscript valuation book c. 1800, available at PRONI D/1514/2/4/16, Hervey/Bruce Estate Papers.
Under the yearly rent roll of Lord Bristol's lands c. 1795 is listed TIRCREEVAN-Caldwell's --18 pounds and the half-yearly rents 1794-1797 is TIRCREEVAN--Messrs Caldwell.
There is an Alexander Caldwell credited with 2 wheels, according to the Flax Premium Returns 1796, and a John Callwell of Drumacardee on the Hearth Money Roll of 1663--definitely before the times you're interested in, but you never know.
There are other Caldwells with numerous spellings, but no other Alexanders or Johns.
Caldwell family wills (1746-1789)are covered in the Tenison-Groves manuscript (T/808/2303-2385 and T/808/2492-2503), but this seems to be the Robert/Luke side. If you are descended from a Robert, this will might interest you:
T/808/2492 - Derry Will made 17 February 1753 proved 23 July 1753
Robert Caldwell of the parish of Tamloughard Co. Londonderry
Land to son William Caldwell who is unmarried, he maintaining testator's wife and children; 15 pounds each to son Robert Caldwell and daughters Margert and Isbell; Executors--John Flimen and Luke Caldwell; Overseer: Rev. Benjamin Bacon; Witnesses: John Lee and John Teylor
I hope this helps. I visited Magilligan in 2006--my grandmother was married in Magilligan Presbyterian in 1899, and it is a lovely area. It really sets you to thinking about what life was like for our forefathers. Good luck.