So I did a bunch of tests and I could not find any settings that gets the desired behavior. Setting the prototype to mineable=false has no effect. Setting the entity to mineable=false makes it so that it cannot be mined by hand, but mining drills can still mine it (if they can mine the appropriate category).
My old method was using a dummy fluid to mine. I forget why I stopped using that method specifically, but that might stop AAI from mining.
AAI miner will need to make some changes on their end to see if a resource ought to be mineable.