After a lot of googling on this - and thinking the crusades might provide an answer - the best I've come up with is [Louis IX][1] of France who died in Tunis on the 8th crusade. That's 920 miles 'as the crow flies'.

By furthest from home, I mean from the monarch's capital city.



  [1]: https://en.wikipedia.org/wiki/Louis_IX_of_France