Your ADAT outputs will send 8 channels down the one cable. Your other sound card needs to accept the ADAT input and you would then use THAT sound cards ADAT connections to monitor the INPUTS coming down the ADAT cable.
I see what your saying and Im thinking the workaround would look like this considering your INPUT mix busses in the MR Console:
MIC 1 >ADAT 1/2
MIC 2 >ADAT 1/2
MIC 3 >ADAT 3/4
MIC 4 >ADAT 3/4
MIC 5 >ADAT 5/6
MIC 6 >ADAT 5/6
MIC 7 >ADAT 7/8
MIC 8 >ADAT 7/8
So on EACH mix group you would ONLY have TWO mics volumes turned up and they would BOTH be output the ADAT pair. You may need to PAN the mics, L/R. EX) MIC 1= Pan hard Left, MIC 2= Pan hard right, then those two would go to ADAT output 1/2. On the other computer you would simply setup MONO input busses coming from the ADAT feed from the MR816. They should show up as MONO ADAT inputs on the other device.
Hope this helps