Our most recent serious testing was with samples of mushroom bedding, before and after composting. These were supplied by Monterey Mushroom in Zellwood, Florida.
Monterey grows the mushrooms in 4' x 8' trays, 8" deep. The trays are filled with wheat straw, chicken manure, and cotton seed meal, along with 2" of peat moss (rich soil). (Sussex Mushroom in England said they use 80% straw.) Monterey incubates the mushroom spores in rye or millet grain.
Each week Monterey produces three compost batches of 28,000 cubic feet. This is neutralized to a pH of 6 to 7-1/2 by adding sugar beet lime (possibly gypsum or alum?).
Monterey wanted to know about the nitrogen in the press liquor, because of fertilizer applications. Pressing this compost was just like pressing peat: only single cell biological mud, no free liquid at all, came through the screen. That happened with materials from both before and after composting. Worse, both materials just sat in the press and co-rotated.
We could not get cake to come out of the presses. We tried two CP-4's and one KP-6, and achieved the same bad results with all of them. Consideration was given to trying a 1/2 pitch screw, or a perforated screen, but it was clear that would not make enough improvement to justify the effort.
The "as received" non-composted material was 67% moisture; the composted, 64%. The press cake of the composted material came out 61%. There was no free water in this material; not a drop could be squeezed from a fist full.
Most mushrooms come from Pennsylvania; mushrooms are Pennsylvania's biggest export.