Well I think we've fairly well confirmed that it was a ridiculous notion to begin with. Lets forget about the original question quickly so that I don't look even more foolish. Some other points worth discussing have come up;
Your priority is to get a relight but the relight envelope for CFM starts from 25000ft. So above that is no relight zon
It's worth dispelling that for any 737 NG pilots. This from the FCTM
The inflight start envelope defines the region where windmill starts were demonstrated during certification. It should be noted that this envelope does not define the only areas where a windmill start may be successful. The Loss Of Thrust On Both Engines NNC is written to ensure that Flight Crew take advantage of the high RPM at engine failure regardless of altitude or airspeed. Initiate the memory portion of the LOSS OF THRUST ON BOTH ENGINES NNC before attempting an APU start for the reasons identified above.