I would find something well short of basing more than palatable; a roster, with me based in DXB, but one that would allow me to break a pattern in a nominated major EK outport, where I could have my string of days off before picking up the return sector(s) of that same pattern 4 of 5 days later.
On returning to Dubai, I'd be quite happy - (well, let's be honest... 'happy' might be a bit strong; let's say 'content') - to do string of flights to and from Dubai, as long as I was allowed to bid for - and be given - a 'compressed' roster to fly my 85 hours or whatever as quickly as possible before I could bid for another flight back to my nominated 'away' port again to take my major set of days off for the month.
You'd probably have to come up with a single 'line' involving ~four pilots who'd nominated the same 'away' port to make this work, and what the company did with these four pilots while they were in Dubai would afford them as much flexibility as they have today.
Of course, this would mean the denizens of the top floor of the Sand Castle would have to drop the ridiculous '14 days' rule, and someone Up There would have to accept that not everyone thinks the Sandpit is heaven on earth where everyone desperately wants to live up to and after retirement.
Singapore Airlines could do it; KAL can still do it; if EK could get their heads around the fact that they could do it too, they'd quickly discover that they'd save more on training than it would 'cost' them (as in 'them', the landlords who are the same people as own the airline) in lost rents and money spent in Dubai's supermarkets. And it would fix the current housing crisis with 100+ pilots and their families living in temporary accommodation almost overnight.