I like the game idea!
Suzanne you could try that - ride in the drops for some many strokes or until you reach that telephone pole or something like and then switch to the hoods or the flats for the same amount of time. Keep your pace smooth and comfortable enough for you to switch between the two positions easily and without swearving(sp) the bike. You could try moving each hand one at a time if you feel steady enough. Pretty soon it'll just become second nature to you and you'll feel "right" in the drops just like you do on the hoods or the flats. I have center pull brakes on mine so I'm constantly moving between the drops and the flats until I can get used to the reach of the brakes in the drops. As for the clipless - welcome to the club. We've all done that hit/slip/hit/slip routine. Funny you would mention that tho - I was just thinking today when I don't THink about needed to clip in, the foot goes right into the clip easy-peasy! When I "think" about it....I miss every time!
Life should NOT be a journey to the grave with the intention of arriving safely in an attractive and well preserved body, but rather to skid in sideways, champagne in one hand, strawberries in the other, body thoroughly used up, totally worn out and screaming: "Yeah Baby! What a Ride!"