Can Sméagol's family tree be tracked all the way to the hobbit families at the time of Bilbo?

Question

When Gandalf explains to Frodo how come the Ring came to his posession, he introduces the tale of Gollum with these words, making it clear that Gollum was related--however distantly--to hobbits:

Long after, but still very long ago, there lived by the banks of the Great River on the edge of Wilderland a clever-handed and quiet-footed little people. I guess they were of hobbit-kind; akin to the fathers of the fathers of the Stoors, for they loved the River, and often swam in it, or made little boats of reeds. (...)

A bit later he explains that Sméagol's grandmother, "desiring peace, expelled him from the family and turned him out of her hole", suggesting a structured society very much like the one the Brandybucks seemed to have (big family with an elder acting as a leader, like this matriarch). Then he says that "even Bilbo's story suggest the kinship", because they understood each other pretty well, knew the same riddles, etc.

This makes me wonder if there is any record that would allow us to trace Sméagol's family tree from the time of Sméagol and Déagol to the time of Bilbo, to see how they are related. I don't know how detailed were the family trees kept by hobbits in their libraries and their memories (or how many generations they involved). Also, having read only The Lord of the Rings, The Hobbit and a bit of The Silmarillion, I don't really know whether this is discussed in some other book, or maybe even in some letter by Tolkien.

Answer 1

There isn't any indication that the Hobbits who settled in that area had any future contact with the Shire and Bree or the Hobbits who lived thereabouts. Given the troubled history of the Gladden Fields and its location between the Misty Mountains and Mirkwood, it's possible that the Hobbits who settled there were driven out or destroyed by the time of the Hobbit and the Lord of the Rings or, alternately, they had remained hidden in that location by not forming the same extensive settlements that the security of a Dunedain-patrolled area allowed the Hobbits of the Shire, but there is no canon indication of one result versus another.

Answer 2

Almost certainly not

Any relationship between Sméagol and Bilbo (or any hobbits of the Shire) would be extremely distant and almost certainly unknown.

Sméagol’s people (who lived by the Gladden Fields) are descended from the Stoors who returned to Wilderland from the Angle hundreds of years before a different branch of the Stoors moved from Dunland to settle in the Shire. It appears that by Bilbo's time, the Stoors of the Shire have been separated from Sméagol's branch for about 1,800 years.

Here is the timeline from The Tale of Years (dates are all Third Age)

c. 1150 The Fallohides enter Eriador. The Stoors come over the Redhorn Pass and move to the Angle, or to Dunland.

1356 King Argeleb I slain in battle with Rhudaur. About this time the Stoors leave the Angle, and some return to Wilderland.

1601 Many Periannath migrate from Bree, and are granted land beyond Baranduin by Argeleb II.

c. 1630 They are joined by Stoors coming up from Dunland.

2463 The White Council is formed. About this time Déagol the Stoor finds the One Ring, and is murdered by Sméagol.

2941 Thorin Oakenshield and Gandalf visit Bilbo in the Shire. Bilbo meets Sméagol-Gollum and finds the Ring. ...

_{The Return of the King: Appendix B}

So the Stoors who lived near the Gladden Fields separated from those who moved to the Shire in about 1150 (Third Age) when the first group went to the Angle and the second to Dunland.

Tolkien strongly suggests that the hobbits of the Shire have little accurate history from before the founding of the Shire in 1601 (Third Age), which was about 250 years after the Stoors of the Angle returned to Wilderland.

About this time legend among the Hobbits first becomes history with a reckoning of years. For it was in the one thousand six hundred and first year of the Third Age that the Fallohide brothers, Marcho and Blanco, set out from Bree; and having obtained permission from the high king at Fornost, they crossed the brown river Baranduin with a great following of Hobbits. They passed over the Bridge of Stonebows, that had been built in the days of the power of the North Kingdom, and they took all the land beyond to dwell in, between the river and the Far Downs.

_{The Fellowship of the Ring: Prologue}

There is no indication that there was any communication between the two branches of the Stoors after 1356 (if indeed there had been any earlier). In which case it would have been impossible for hobbits (either in the Shire or the Wilderlands) to track their relationships.