Okay, here're the issues at hand:
1- It's a good idea to give more time for competitions.
2- It is NOT a good idea to give A LOT more time for competitions. People forget if you put the deadline too far off. One month is plenty of time to write a prompted composition. Perhaps stretching THAT to a bimonthly competition is a good idea.
3- If we were to incorporate another regular-per-amount-of-time competition set, it'd get confusing what with the other set of competitions (the monthly ones) going on concurrently. Perhaps if you instead proposed it on a quarterly/seasonal basis rather than "every three months." Be easier to distinguish, even though it's still a little odd.
4- The judgment guidelines you propose are pretty bad (no offense). They're rigid and confining and could seriously undermine creativity, artistry, and real music. You say you don't want the criteria to be subjective? Music is a subjective art. Those guidelines are on the wrong side of the dichotomy presented in Dead Poet Society, where greatness of art is quantifiable.
5- If we decide by majority vote what sort of composition is to be done, we run the risk of having the exact same competition every three months. Sure you have more participation, but you also have less variety.
My .02