It’s not only your home team’s games that are blacked out on MLB.tv. It’s also any nationally-televised game, like the Wednesday night games on ESPN, and the Saturday afternoon network games. And because the whole playoffs are nationally televised, you don’t get to watch those either.
I get around this by using Unlocator.com, which is a DNS service that makes it appear as if i’m outside of the United States. This allows me to get all games, including the playoffs. It also allows me to watch streaming services that i would not otherwise be able to get in the United States, such as the BBC iPlayer service, and shows from the ABC and SBS in Australia, and a whole bunch of other stuff from various countries. It costs 60 bucks a year, but for me it’s been worth it.
There’s nothing illegal about the service, and you’re not violating anyone’s copyright. You’re simply fooling the host servers into thinking you’re in a different location by using a particular Domain Name Server. It would actually be pretty easy for sites like MLB to block this sort of thing, and the fact that they haven’t suggests that they don’t consider it a very big problem. I know people overseas who use it to get the US version of Netflix, which has more stuff available than Australian or New Zealand Netflix.