The available voltage is 10.5 volts at 350ma. The needed output voltage is 3.3 volts at 800ma. The 800ma is needed for 60 seconds. The purpose is to supply power to a module while it goes throug a shut down sequence.
OK. You have 3.7 watts available and need 2.7 watts at 3.3 volts. A simple switcher will do the job. Have a look at National Semiconductor or just go to the nearest Radio Shack or Conrad, if in Europe, and buy a module that does what you want.