Rigol DS2072A-S shows traces at 24.31 seconds. Also could not find anywhere it shows the number of times booted.
Agilent U1233A multimeter took about 1 second for most settings.
Can you enter the contest once per month or only once? Either way, very cool idea. I made the mistake of getting the Rigol scope with the builtin function generator and regretted it almost immediately, just not enough to send the scope back and go another 2 weeks without it. Would be awesome to have a standalone AWG.