Yeah, you have to be ready to actually leave and not just bluff. I can tell you straight-up that once I actually left for a month, they started to send multiple come-back letters slashing my price to almost half. The fact that they could have simply been charging me less the entire time with no problem was what pissed me off enough to try to keep going without Wi-Fi and now it's been over 2 years and counting. I've visited a lot of interesting libraries as a direct result!
What games are so specific as to require the same IP? If you can try lasting just a month, they will absolutely offer you discount deal to return.