I have had the supervisor (who went offline for 20 mins before returning and confirming) do it on an AKL to IST once under almost identical circumstances - a month out, and we were the only ones in F at that time.
As others have said here, EK manages its inventory very tightly and knows when it can sell a seat and when it likely won't, so I think it will depend very much on the route.
I think it is reasonable to ask once or twice - but if you get knocked back again I wouldnt bother - they will be saying no because they think they will sell it.