Not sure if you have seen that a William Burgess of Kirkland was listed in the Urr Horse Tax Rolls 1797-1798 (1 horse)
Map~ http://tinyurl.com/2ufpe343
Little Kirkland, Meikle Kirkland and Kirkland Burn are all mentioned as in Urr in the 'Place names of the Stewartry' website http://www.kirkcudbright.co/index.asp
Gadget
Ah yes, thankyou! I'd forgotten about that we must have discussed this connection some years ago.
We visited the Parish Church at Urr in 2016 and found a headstone for John Burgess and his wife, but it was unreadable and we are not sure if there is a connection to Catherine.