An easier way would be using translocators. A diamond shard on the input to make sure it only has one of an item at a time, a filter on the output so it doesn't pull anything but what you want out.You can automate with an ME network. Barrel with BC gate set to pulse ONCE when there is room in inventory (the altar). It pulses once, moves stone to altar. Set precise import bus to remove slate when it reaches the desired level. Slate gets removed, gate sees change in the inventory, checks spaces, pulses once, starts process again. Standard mob farm with well of suffering to power the automation.
An even cheaper way would be using a TC golem (especially now that you can get their research within a few minutes of starting TC). Straw golems can only carry one item at a time, so they're perfect for the input, and you can use anything capable of using filters for the output (such as more golems or itemducts).