I did the math, too, and came up with a different number than you. If my calculations are correct, to get the gem reward, you need 750 brooms, 750/8 per respawn=93.75, which would be 94 times you would need to collect 8 brooms during the event. The event lasts for six days, I believe, so 94/6=15.625, which is essentially 16 times per day it would be necessary to collect 8. So, theoretically, one could collect only during their waking hours and still get the gems, as long as you collected almost every single waking hour of every single day. I'm not saying that it's reasonable, mind you, just that it's possible.
As long as I'm calculating anyway, 40 gems is $1.99, so for all this work, one would be awarded 5 gems, which has a street value of 25 cents. Seriously. In the same vein, I notice the mini-event leaderboard awards have also gotten similarly crappy since The Incredibles event ended.