Isn't it possible that more mundane issues such a large increase in caseloads might also justify an increase in the number of justices?
What was the actual (as opposed to neo-confed-supplied) reason for Lincoln's alleged desire to increase the number of justices?
I presume you are aware of the importance of a single justice in 5-4 decisions such as the Prize Cases (1863) (the 5 in that case included 3 justices named by Lincoln) in 1862. The tenth justice was authorized shortly before the Prize Case decision. The court had dropped to 6 members in April 1861 before Lincoln named 3 new members in 1862.
Here is one take on the reason for adding the tenth justice [Link]:
By 1863 the Supreme Court confronted a number of important war-related cases, and the Republicans were naturally anxious for the Court to affirm the legality of the Lincoln administration's actions. Addition of a tenth justice, who would be vetted for sympathy to the Union cause, would solidify a precarious pro-administration majority.[8] The man who assumed this post, Stephen J. Field, had turned down the California circuit judgeship made vacant by McAllister's resignation, with the reply that he "preferred to remain Chief Justice of the Supreme Court of the State than to be a judge of an inferior federal court." He had generously hinted, however, that "if a new justice were added to the Supreme Court of the United States, I would accept the office if tendered to me." The administration evidently took no umbrage at this audacity: when in 1863 Congress authorized the tenth justiceship and abolished the circuit judgeship, Lincoln offered the Supreme Court position to Field. Even though Field was a Democrat, he appointed him on the assurance that Field was a fervent Unionist.
Have you been able to find the reasons why the Republican Congress did not increase the number of justices above 8 when Johnson was president, but increased them to 9 after Texas v. White (1869) when Grant was president? Did these changes in the number of justices have to do with a decrease in caseload followed by an increase in caseload or simply with practical politics?