People call something a "conspiracy" when they want to delegiitimize it without actually doing any work to demonstrate that it is incorrect.
"Conspiracy" can encompass a wide scope, depending upon what you mean by the word. Is the teachers Union a "conspiracy"? Sort of. It's a group of people in the same trade attempting to increase their own income and minimize their own responsibilities.
Surely as a conservative you are familiar with Adam Smith? Adam Smith said a lot of profound things, but none more profound than this.
People of the same trade seldom meet together, even for merriment and diversion, but the conversation ends in a conspiracy against the public, or in some contrivance to raise prices.
This has proven to be an all too common occurrence when the issue is money.
In 1861, the issue was money.
Your theory that a secret shadow government has been in charge since the 1800s is just not historical. You may as well claim the masons are in charge.