Payne's plane slowly lost it's pressurization, the pilot(s) passed out, and it flew on auto pilot until it ran out of gas and crashed. There were F16's that intercepted it to see what was going on. The reported fog on the inside of the windows, which indicated loss of pressurization.
Jake, depending on how heavy/light the airplane was, it could climb at 1-2,000 feet per minute from 350 to 450. So maybe 5 minutes. But much less if you 'zoomed' it up there by pulling back harder, but you'll bleed off airspeed if you do that, and you won't stay up there long before you run out of airspeed and come right back down, which might be why they dove down to 230.