We have snowshoe hare here as well, it's our only "rabbit" species. They fall to pellet rifles far easier than squirrels. I've taken them with one shot kills with .177 rifles shooting below 500fps (canadian model Crossman Springmaster), with both head and vitals shots. Their dance lasts longer when shot in the heart/lungs, but not more than 30 seconds. The caveat is, if they're shot in a non-vital area, the adrenaline rush makes them very hard to finish, so shot placement is absolutely key. The headshot is best.
Now that I own a more powerful rifle, they're the easiest quarry in the wood. If you can shoot accurately at distance, it really only takes about 5fpe to put'em down quick.
First time I killed one, I was so surprised. As the shot left the springmaster, I was sure I'd pulled it, and put a nonlethal shot into it's hindquarters. The hare leapt about 3' into the air, landed on it's back, flopped around vigorously for a few seconds and then....just....stopped.... I nearly fainted! Good eatin!
J