A close-in hold with a minimum holding height of around 7,000' (a la Lambourne at Heathrow) that serves both runways with approx 20 NM of vectoring ex the hold to touchdown* (*translation = constant descent to touchdown) would minimise the problem of a runway change in busy periods (and a lot of other problems too!).
There's even an aid available for such a hold at DXB - the Sharjah VOR.
Dubai's getting close to being as busy as Heathrow every night during the midnight arrivals rush. If the close-in hold works so well and seamlessly for Heathrow, (arguably the best ATC in the world), why wouldn't it work for Dubai?