If you move the rightmost conduit one tile up and to the right it will crash after two outputs.

This is the closest I have seen to cardinal chaos and I love it.  The LexC of this solution is in the title; it takes 6 outputs before it reaches its 4/15P steady state.  The general idea is that atoms from dispersion enter a circuit of length 11 in pairs.  Any atom eventually ends up calcifying, converting to fire, and triplex bonding to its neighbor.  Meanwhile dispersion is just attempting to proc every tape loop, and whenever enough pairs have become outputs the circuit is close enough to empty that it will succeed.

My original design was 41 and the circuit was a hex arm and a piston, with no conduit.  The piston had way too much work, 20 of the 41 instructions.  After a complete layout change I got to 31, then 28, then 26.  I don't imagine that it goes too much lower.