I've been trying to hook my Smith line to Deacon Joseph Smith and Elizabeth Cone. Your mention of the Tyler family connection makes it seem all the more likely, but still elusive.
Perhaps if we share information about the children of that family, we can help each other.
I show these children:
1. John Smith 27 July 1736 Haddam m. Elizabeth Tyler
2. Lucy Smith 26 Nov 1738 Haddam m. Eliakim Brainerd
3. Joseph Smith 22 Dec 1741 Haddam
4. Charles Smith 28 Jan 1744/45 m. Mary Williams
5. Elizabeth Smith 26 Apr 1748 Haddam
6. Aaron Smith 23 Feb 1751 Haddam
7. Joshua Smith 23 Feb 1754 Haddam m.?Knowles?Shailer?
8. Baby died 1760, age 8 months

I'm trying to make the link between my Joseph Smith born abt 1790 in Haddam (who married Betsy Fowler of Suffield) and Joshua Smith born 1754.

In New Town House Hill Cemetery, there are buried:
Joshua Smith, died Apr 3, 1836, age 83
Olive Smith, wife of Joshua, died Mar 5, 1847, age 90
(I believe Olive's maiden name was Shailer.)

Also my definite relative is buried there:
Joseph VanDeusen Smith, died Oct 30, 1888 age 76
Charlotte, wife of JV, died Feb 4, 1864 age 51
Tyler W. Smith, son of J. and Charlotte,died 1835, age 13 mos.

Please email me at miamoja@aol.com and maybe we can pursue this Smith line together.
Ruth