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?
"There are three vacancies on the bench of the Supreme Court ---two by the decease of Justices Daniel and McLean, and one by the resignation of Justice Campbell. I have so far forborne making nominations to fill these vacancies for reasons which I will now state. Two of the outgoing judges resided within the States now overrun by revolt; so that if successors were appointed in the same localities, they could not now serve upon their circuits; and many of the most competent men there, probably would not take the personal hazard of accepting to serve, even here, upon the supreme bench. I have been unwilling to throw all the appointments northward, thus disabling myself from doing justice to the south on the return of peace; although I may remark that to transfer to the north one which has heretofore been in the south, would not, with reference to territory and population, be unjust.
During the long and brilliant judicial career of Judge McLean his circuit grew into an empire---altogether too large for any one judge to give the courts therein more than a nominal attendance---rising in population from one million four hundred and seventy-thousand and eighteen, in 1830, to six million one hundred and fifty-one thousand four hundred and five, in 1860.
Besides this, the country generally has outgrown our present judicial system. If uniformity was at all intended, the system requires that all the States shall be accommodated with circuit courts, attended by supreme judges, while, in fact, Wisconsin, Minnesota, Iowa, Kansas, Florida, Texas, California, and Oregon, have never had any such courts. Nor can this well be remedied without a change of the system; because the adding of judges to the Supreme Court, enough for the accommodation of all parts of the country, with circuit courts, would create a court altogether too numerous for a judicial body of any sort. And the evil, if it be one, will increase as new States come into the Union. Circuit courts are useful, or they are not useful. If useful, no State should be denied them; if not useful, no State should have them. Let them be provided for all, or abolished as to all.
Three modifications occur to me, either of which, I think, would be an improvement upon our present system. Let the Supreme Court be of convenient number in every event. Then, first, let the whole country be divided into circuits of convenient size, the supreme judges to serve in a number of them corresponding to their own number, and independent circuit judges be provided for all the rest. Or, secondly, let the supreme judges be relieved from circuit duties, and circuit judges provided for all the circuits. Or, thirdly, dispense with circuit courts altogether, leaving the judicial functions wholly to the district courts and an independent Supreme Court"
That was from Lincoln's December 1861 message to Congress. In 1862, the judiciary was organized into 9 federal circuit courts plus the west coast states of California and Oregon. Those states were organized into a 10th Circuit and a 10th justice was added to oversee it.
But that explanation isn't as much fun for you as attributing evil intent to Lincoln, is it?
Vindictive politics, actually. The radical Republicans actually reduced the size to 7 justices by passing the Judicial Circuits Act of 1866 that said the next 3 justices to retire wouldn't be replaced. They didn't want Johnson naming anyone.