Theory says 9 2.  I wasn't even able to get a single output on 9 if I restricted myself to the first and third inputs, though I had a few close calls.  Obviously I couldn't get two clones of that pipeline to fit.

Giving myself the first and second inputs to work with, 9 came easy on a 4 cycle loop.  Then it was a question of getting better than 9 [4].  My first design threw away water, but the only way I could use it was as an odd one out pipeline, which wouldn't beat 9 [4] until the 6th output.  Getting something that beat it earlier was my goal.

There is the idea of a 9 3 by using the first input water and one of the third input salt to get faster animismus on the 2nd output.  I didn't have any geometry for it, but I believe it is probably possible with some kind of automated search.  Instead, I used first and third input water to get faster animismus on the 3rd output.  This was the first layout I found where it was possible to run animismus every 3 and not cause horrible problems.  Instead it only has mildly annoying problems in the position of arm 1.  That's why it isn't full throughput.  But still, 9 4 3 4 beats 9 4 4 4.  If it gets beaten by 9 4 3 3 it's kind of expected.  If it gets beaten by 9 3, I'll be impressed.  If it gets beaten by 9 2, I'll go sulk for a bit.