To me, a #6 lead load is an appropriate load for prairie chickens, sharp-tailed grouse, and even huns. Here are 20- and 12-gauge reloads that I've shot all those birds with. Of course, you need to choke your gun for the normal distance of your shots.
Here are a few of my pattern numbers with the loads I've shot them with to give you an idea of the kind of patterns you may get with different choke constrictions.
Patterning results from a 20- & 12-gauge Browning Citoris with 28" Invector-plus barrels using Briley flush chokes (patterns average of five, 30" post-shot scribed circle, yardage taped muzzle to target, and in-shell pellet count average of five).
20 GA 2 ¾” RELOAD (BLUE DOT)
1 oz #6 lead (233 pellets) 1200 fps
30 YARDS – SK / pattern 147 (63%)
30 YARDS – IC / pattern 168 (72%)
30 YARDS – M / pattern 200 (86%)
40 YARDS – M / pattern 146 (63%)
40 YARDS – IM / pattern 163 (70%)
40 YARDS – LF / pattern 164 (70%)
40 YARDS – F / pattern 159 (68%)
40 YARDS – XF / pattern 171 (73%)
12 GA 2 3/4" RELOAD (GREEN DOT)
1 1/8 oz #6 lead (267 pellets) @ 1225 fps
30 YARDS – CYL / pattern 147 (55%)
30 YARDS – SK / pattern 171 (64%)
30 YARDS – IC / pattern 211 (79%)
40 YARDS – LM / pattern 173 (65%)
40 YARDS – M / pattern 182 (68%)
40 YARDS – IM / pattern 195 (73%)
40 YARDS – LF / pattern 205 (77%)
40 YARDS – F / pattern 198 (74%)
50 YARDS – F / pattern 138 (52%)
Hope this helps, good luck!