Just saw this, thank you! I'm honoured to be listed alongside these insightful forecasters — and thank you for running it. I found this competition very fun and motivational, and think this kind of thing works well for fixing some incentive problems. 

I can't say why more people didn't submit, but I can say what did help prompt me to submit two rationales:

• Being aware of it: I checked the EA Forum when your announcement was near the top, which was fortunate because I often miss valuable posts here when I'm busy. 
  • More publicity would help, but I also think that having a way for people to 'opt in' to the competition when they see it would be good. I set my own reminders to do it, but I imagine others intended to participate but ended up forgetting.
• The sense that it required a relatively small time-investment in proportion to the likelihood of winning a prize
  • I think it's good knowing your rationales don't need to be perfect/comprehensive/outstanding in order to receive a prize
  • Allowing/expecting people to submit multiple entries helps for this, as it meant I didn't need to worry too much about choosing the ideal question; being allowed just one entry can be off-putting I think
  • Similarly, offering $4,000 across a maximum of 15 prizes stopped me from being ambitious and perfectionistic — the timeframe given was also good for that. However, it's quite odd to be motivated by small prizes, and I expect people may have been put off by the small-ish reward

Finally, I expect another reason why the timing may have led to fewer entries was because Future Fund applications were due 10 days later (that seems like a long time, but I know that its approaching deadline was on my mind when I submitted my rationales).