Roster Change, GMDS pretty well covers most of the points at issue. I can vouch for the fact that I'm in no fit state to start duty on a return ULR flight after only one day's break from the previous ULR flight. Virtually every member of the crew turns up for duty having been unable to sleep before the flight, and very few manage to get any meaningful sleep during the whole layover. (Most collapse into bed on arrival, only to wake [if they're lucky] a couple of hours later, and that's all the sleep they get for the whole layover.) The crew that have to operate for the first part of the sector really suffer. (One positive: the crew that takes first rest have absolutely no problem getting to sleep!)
The rules even spell it out clearly - any crewmember rostered for a ULR flight must be acclimatized, (i.e., two local night's rest) before commening duty. However, EK convenientely (mis)interprets this to read "before a ULR pattern", and has the crew operate the 16+ hour return flight after only 24 hours break from the outboud 16+ hour flight.
Another point, the importance of which cannot be overstated is the need for SITTING as well as horizontal rest. It's just not possible to "rest on demand" and get any semblance of quality rest in a claustrophic bunk - where the ceiling is too low to even sit up in the bunk - at 9.00 am "head time", and where geting from your "rest" area to a toilet involves a major exercise - where you often as not have to line up for quite some time to use the toilet, unless you want to walk the whole length of the aircraft (if you can get past the food carts blocking the aisles).
And after that, you can forget getting your head back into any semblance of "rest".
Half way home on the return sector of my last ULR flight, neither the FO nor I could work out where our body clocks were at.