> im ending up with 263Ohm
For 200 ohm goal, for any reasonable number of inputs, the answer should be "somewhat more than 200 ohms".
For a Hundred inputs the answer degenerates to infinity. (20,000/100 is already 200 ohms.)
Half a Hundred inputs is already 400 Ohms, another 400 ohms added makes 200 Ohm goal.
So just throwing darts, a fourth of a hundred inputs will be significantly bigger than 200 Ohm loading, but much less than 400 ohm loading. Perhaps 250? 300?
The "200 Ohms" is not critical. Mike amps work fine 150 to 300 ohms. If the "right answer" is 263, not only is 270 "exact enough" (mike amp sees 204 ohms), 220 or 330 will work also (giving 174 or 236 seen by mike-amp). Just do both channels of a stereo mix with the same value (5% is good, 2% is now cheap).