My girlfriend, from Toronto, used to move to different networks about once a month just to catch a big game for the Blue Jays. Of course, we finally just landed in Mobile, Alabama (Braves, Rays, and Marlins (and now I'm hearing the Reds can be seen in that territory) because we knew the Rays would play then 19 times a year. Then, ultimately, we wound up in Charlotte (Braves, Orioles, Nationals, and Reds) because I was excited about the Nationals, wanted to keep access to my home Braves, and knew we'd catch 19 games a year with the Yankees, Rays, Red Sox, and Blue Jays on MASN. It worked really well. However, if she moved to Detroit or Oakland or somewhere to get the RSN so we could see the Jays, we never had any problem.
I am now a subscriber to Multi-Sports package but, you know, I'm not certain about your question. If the Hurricanes are playing the Blue Jackets, you'd think I'd have access to the game on either network, but, just out of habit, I only check the Hurricanes home network.
Anyways, I only caught a few Reds games on the alternate sports network and was told I'd need the Multi-Sport package to get most of the games. I've also been told I can catch a few innings every now and then when somebody goes into extra innings, etc. It's worked somewhat on NBA and NHL but I'm afraid, for the most part, the games stay within the blackout period.
As for moving, though, I probably wouldn't do it EVERY time they played a different team (as that's a lot of moving). On the flip side, though, I really wonder how much they care. As long as the bill is paid, I'm sort of willing to bet they don't. ALSO KEEP IN MIND: You can order WWOR for just $1.50 and they show around 20 games a year.
Cade