Negotiate better terms. I work for a FANG, and my salary is pretty consistent with what's in that list despite the fact that I work from home elsewhere. Sure it's northeast, but that's probably closer to southeast than to west coast at this point. Maybe in southeast you'll take a bit of a salary hit, but probably still make quite a bit more than you can get locally.
There are a couple of other downsides, though. One is that you'll probably only be mostly remote. I travel one week a month, which my family can tolerate well enough (one kid in high school) but if your need to be with your family is greater then that could be a bigger issue. The reason I do this is because of downside #2: being the only remote in a team sucks in 90% of cases, even more at FANGs which tend to have extremely remote-unfriendly work flows/habits. A lot of people just can't be weaned away from hallway (across the desk, lunchtime) decisions, nothing written down, each outcome typically presented as a no-longer-debatable fait accompli days or weeks later - no matter how much it screws you or anybody else. Questions asked online get answered hours instead of seconds later, if at all. Code reviews take days instead of hours, again because everybody's attention is exclusively on what's happening in person and also because of time-zone issues which you can't avoid no matter how well you've educated your colleagues. Get used to working west-coast hours at least half the time no matter where you really are, and expect to get dinged on reviews because you can't complete anything collaborative as fast as your peers (short of being such a force of nature that you can overcome the entire org's resistance to change in this area).
I know that sounds pretty dire, but that's how you'll earn those big (by local standards) bucks. Only you can decide if it's worth it. Good luck.