The population of Nevada in 1870 was about 43,000. Over 12,000 people voted in the statehood referendum in 1864. Your 15,000 population is wishful thinking, as is your conspiracy about Nevada statehood to begin with. Lincoln got 212 electoral votes in 1864 to McClellans 21. He didn't need Nevada's three.
Congress and the Lincoln administration, however, saw Nevada statehood as additional support for the 13th Amendment to the United States Constitution (which outlawed slavery) and for Lincoln's upcoming reelection. The U.S. Congress quickly passed the Nevada Enabling Act in March 1864 and by summer a new constitutional convention was convened.
Here's another source that mentions Nevada's inadequate (for statehood) population (State of Nevada, Department of Cultural Affairs):
Thus, Nevada, with a population less than required for statehood by the Northwest Ordinance, entered the union as the 36th state. The designation "Battle Born State" is appropriate inasmuch as Nevada's entry was a result of the Civil War and the accompanying problems.
Lincoln was nothing if not a schemer.