Maybe allow only to post prediction on the first 2 weeks of the month. 1st week first prediction then 2nd week for the final prediction so that it will not be unfair for those who predict earlier and the result will be more exciting and luck based rather than the current result since the price usually sideways already during the last week of the month.
The word unfair is not necessary because participants have the freedom to put there predictions at given time. Some users just rushing things to vote while other is taking there time to vote just to have a better view for the price prediction.
You have a point that making the time of prediction far to the result day will give a more luck based results because it will be very hard to TA the price of Bitcoin for two weeks period compared to the current rules which only 1 week time span.