Hi Cheryl,
What a nice surprise to stumble across this post (this is Jo, the 'fellow researcher' you mention).
I thought I would post a few points that might be relevant to help establish links:
Firstly to clarify some details surrounding Mary Ann Carter b. 1856, aunt of Clara Carter.
This is not the same Mary Ann Carter est 1848 (nee Smith, previously Coy who is a direct ancestor of mine).
Mary Ann Carter b. 1856 is the daughter of Thomas Carter est 1797 and his second (much younger!) wife Elizabeth Goodband (both Mary Ann and Clara can be found with Elizabeth on the 1881 census in North Kyme). Thomas was also the grandfather of Thomas Carter est.1846, my g-g grandad, who married Mary Ann Coy (nee Smith)
This family connection to Harriet Smith's Gray family is part of the circumstanial evidence I have come across that suggests my Mary Ann Smith was Bathwell's and Charlotte's daughter.
Since we last spoke I have also visited the church at North Kyme and seen the gravestones for Henry and presumably his mother Charlotte Smith (they are next to each other and next to numerous Gray gravestones, from Harriet and Abraham's family). In a neighbouring plot is also the grave of Lucy Martin, sister of Thomas Carter 1846 which also points to a link to my ancestors. On the basis of the details on Charlotte's headstone I was able to track down her death certificate, on which she is described as the widow of Bathwell Smith and the witness is named as her daughter Harriet Gray (if you are interested I would be more then happy to send you a copy).
From census returns:
Heckington, 1891; A Bartley Smith b. 1864 (Lincolnshire) is with Phoenix (who I believe is also a brother of Abraham) and Lydia Gray but with no relationship named.
Donnington, 1901; A Thomas Smith b. 1881 (lincoln) is with William (who I believe is a son of Harriet and Abrabham) and Sophia Gray named as nephew.
Thomas Smith, would actually be the cousin of William Gray, if the links are you think but I guess as he was a bit younger it may well have been a respect thing.
As my Mary Ann Smith and Thomas Carter had such a big family, I'd be grateful if you could post the names of any other mourners mentioned, so I could cross check them against all the names I have.
Hope that all makes some kind of sense, have to admit my head starts spinning whenever I look into this family!
Best wishes
Jo