Hey Archie, I did not look at the ZP3 output spec before I posted (but should have),. It is posted as 41db of gain (not a specific V out which would certainly be dependent on the source driving it). I guess I was assuming that since most of Steve's amps are in the 1.5-2V sensitivity range that for a typical 5mv cart input you would get an output in the ~1.5V range. Should have done my math first.
Regardless though, you are correct with your math. I do get .56V for a 5mv input at 41db of gain. Not a 100% sure on your discrepancy though. Possible that the carts are outputting a slightly different amount than the pub. spec.
I too ran my .04mv cart straight into the ZP3 (just to see) and yes, while the gain can be made up with a traditional Preamp, like you found out there is a lot of inherent tube/circuit noise that gets revealed in the process. Like everything in this hobby, especially when your components have sensitivity specs, working or not depends on a lot and on match up those sensitivites. Speaker, amp, pre sensitivity are all going to play a big role.
My thought is that the ZP3 will work best with carts @ 5mv of output and an amp that is on the higher sensitivity side, certainly no lower than 1.5V (ie, <1.5V) for full output. In so many cases, we rarely listen to 'full' output though so I imagine that the less than ideal or matching specs on paper don't really always come into play, though if you can match it up proper then it will definitely benefit the noise floor coming from the ZP3 as we both know. Check out the following link. It has some good calculators and ratio descriptions,..
http://www.sengpielaudio.com/calculator-gainloss.htm