Nl,
I think you and others have sorted out and come to more or less same conclusions I have.
I think you are right that Agnes was a child Rebecca and Abner as Eliza was too old in 1865.
I also think Rebecca and Abner did not marry and that was reason Eliza left and went to live with Brothers.
I have Parsons line from Eliza and her siblings back to 1500 and it connects to other Parsons on bcc.
I will insert later but in short Eliza's parents were Rueben/Littley Parsons * born 1773 Halesowen and Ann Harris born 1770 Halesowen ( They married 3/6/1793 Clent)
parents of Rueben were Jason/Littley Parsons and Sarah Baker who married 26/9/1770 RR
Eliza had about 8 siblings of which Samuel born 4/7/1802 Halesowen and Rueben born 1812 Halesowen were two brothers she went to live with when she left Abner Harris.
As noted before I have a complete data base of Parsons family in Black Country ( 3000 plus names) and can look up any Parsons connection.
* In case you were not aware a lot of Parsons were noted on records as Littley alias Parsons or Littley/Parsons