How to ask PhD advisor to work remotely on thesis for extensive periods?
I think you should aim for a shorter period at first, to show that it doesn't affect your productivity.  My wife and I aim to both work remotely 25% of our time, to address the two-body problem.  If each of us works remotely for two weeks every two months, that aim is fulfilled.  A colleague of mine just returned from a 10-week remote work trip. 

Six months, however, is very long to work remotely in one go.  It is of course more expensive to work remotely in shorter segments, but if your advisor doesn't know yet whether it will work out, six months is too long.  Explain that you are ultimately interested in working remotely up to half of the time.  Propose to work remotely for 3-4 weeks first.  Be available at any normal local time for your supervisor, even if that might mean inconvenient times on your end.  After the remote work trip, return and evaluate how it went.  Then propose to plan a longer remote-work trip, perhaps 10 weeks, and return again.  If all goes well after a couple of 10-week blocks, you could bring up the idea for an extended six-month period.

The worst that can happen is that they say no, and you may have to find a different way.  Perhaps they don't agree with 6 months in one block, but are fine with 3 2-month blocks spread over a year.  It will cost more money, but it is safer in many ways too.

Good luck.