I haven't hunted grouse in the last few years really, but, I know I would feel ill-equipped with a 22. I find an open-choke 20ga to be pretty good for those in thick bush, the last few I shot was with a 20ga Wingmaster with a 21", CYL barrel, #7-1/2 shot. I know that in the last 2, one had no pellets in the breast, one had 2. The spots I hunt in normally see a fair bit of pressure, just never feel I can get in 22 range. Or, I don't see them and flush them. (ground, or even off of high, overhead branches.
But if I was suggesting a 22...
I'm personally a huge fan of the Tikka T1x, and have a 20" barreled one. It's an accurate gun with a wide variety of ammo options. SS and high vel. (a first for me personally) I've not shot, or even held the 16" barrel version, but I'd be considering one of those if I were the OP. A CZ 452 Scout would be a tempting back-up plan ($500-$600-ish used) and I've come very close to buying one of those a number of times.
I would be paying close attention to the trigger (light enough?) and put a decent scope on it-whatever you get. I've owned some cruddy scopes in my day, and I think trying to see/hit a bird like that with such a good camo game=not the time for a $50, fuzzy scope. The vintage Bushnell scopechiefs/banners are pretty tough to beat for the $, and the "command post" feature on some of them makes for some quick targeting. Once had a fixed, 2.75X and have been searching for a decent one to replace it ever since. lol