Think the OP needs reminding that:
- When 1 engine starts, you are NO LONGER in the "Loss of Thrust on Both Engines" scenario;
Thus, repeat of procedure is only required using BOTH levers if NO engine has successfully started. Until an engine has relit, the procedure loops itself indefinitely.
Why would you only try and repeat a few times? The lower you get, the thicker the air, the more higher concentration of O2 and the more likely it is to have a successful restart attempt. For those who need reminding,
Speed bird 9 was successful relighting the first of 4 engines only below 13,000' as the crew kept trying to relight the failed engines (due volcanic ash). Had the not been able to it would have been the first 747 to ditch. It pays to keep trying until the very last moment, one engine is all it takes to avert disaster.
So split the flight deck duties:
LHS flies/glides, keeping aloft as long as possible until a (no engine available) landing spot has been successfully been identified and is within reach;
RHS continues to try and restart engines, read QRH, actions drills and advises if there is a requirement to "dive for speed" only when QRH dictates...
Don't rush, give yourself more time by staying aloft longer and preparing for the worst rather then diving down.