So people spamming the closes and easiest number that they can has always been a problem for map voting so far as i can see, and the CMG servers use a rather annoying brake where one cannot move where as the dogz servers just hope you will vote like a good boy. Instead of adding a time to vote, why not just utilize a time that is unused? The end of a game when everyone sits there as the winners name is displayed and music plays is a fairly long break that i think would be fine to vote in.
To the point version:
Basically, could map voting just occur at the end of a game? There is already a break, which would help end the convenience spam as there is nothing better to do during the time.
I'm more for the "give a short session of time for everyone to vote and not be able to do anything but vote during the game" but I like what you're thinking with this and would consider it worth a try.