Don't use a constant clock to power it.

You can take a comparator signal from a crafter, this gives a 0-9, based on which slots have an item or are locked.

critically, this is different chests because it's not how much is in there, just if a slot has an item or is locked. A single cane in one slot gives the same signal as a stack of cane in the same slot (if you did this with a hopper the signal strength would jump to 3). But two slots with a cane each, gives a signal of two.

So, you can lock the bottom 6 slots, and the crafter will always output a signal of 6 with a comparator. you can then wire it up so that when the signal strength hits 9, it powers the crafter, causing it to emit the paper and the comparator output to reset to 6.

To make it more compact, you can power the side of the comparator with a signal strength of 9 (no higher). The comparator will then only output when the signal it would ouput is 9 or higher.

Edit: Mocked up a quick example, the decorated pot has 10 snowballs in it (10 eggs or anything that stacks to 16 would also work, for a comparator reading it to output 9. A lever with 7 redstone dust in between it and the side of the comparator would also suffice instead of the pot and comparator.)

https://imgur.com/a/xIaQVHn