Under 72 hours!
Here's my new itinerary:
Dec 6 IB 7500/IB 7626 ORY 7:25PM DXB 8:35AM 10h 10m via LHR
Dec 8 IB 7629/IB 7443 DXB 2:35AM MAD 10:50AM 11h 15m via LHR
Dec 8 IB 3176/IB 7626 MAD 1:25PM DXB 8:35AM 16h 10m via LHR
Dec 9 IB 7573/IB 7507 DXB 10:05AM ORY 6:40PM 11h 35m via LHR
€304.00
Pretty much a full day to explore Dubai, and less than 3 days out and back. There's flexibility in the MAD-LHR leg; I opted for more time in LHR so that there's less chance of missing the second flight to DXB, plus IIRC they have nicer lounges there.