It's nowhere near as fancy as yours, but it's a start!
The gate is set to emit a redstone signal (carried via redcrystal, because I find it so much easier to use) when there's an item in the inventory or when the LP is below 25%, so it only turns off the redstone signal when it's got enough LP to make a reinforced plate, and when there's room in the altar to put it in. This means the golem is only active for the moment it takes it to move the item from the chest next to it, to the altar, so it won't get off of the fetter. Otherwise, it will put stones in the altar when there's not enough LP, and waste some of it
The currently deactivated golem is set to put 1, and only 1, either of livingrock or a botanical slate. I'm thinking I may drop the livingrock from it, as botanical slates are easier to automate and use less LP!
The last golem is set to extract reinforced slates, and only reinforced slates. My next step will be to set up more fetters with Golemic Inhibitors from Automagy, set to individual golems, that will each be set to take out a different slate. I'll then stick levers on them, similar to your design, and voila, I can define which type I'll be making!