I think a lot of you guys are looking at this from the wrong angle. The reason 5cp can induce stalemates is not due to the configuration of how round timers work, and thusly changing said configuration won't suddenly vanish the need to stalemate.
Sideshow said it best in his Some Flaws with 5cp video. The reason teams would (and frankly should) rather stalemate than push is because without a big advantage, you are putting yourself at a disadvantage when pushing just because you're more likely to make a mistake pushing as compared to holding. Teams chose to stalemate because waiting for your opponent to make a mistake when they push involves less risk than pushing yourself.
For example, in equal uber situations, using your uber earlier than the enemy team is seen as putting yourself at a slight disadvantage, however TF2 is designed in such a way that in order to push against a team that defends well, you will almost always have to use your uber first. This means that in such a situation, you are taking a risk by simply trying to push. Let's not forget about all the other things that can go wrong when pushing that can lead to a failed push attempt and a successful counter-push from the enemy team.
Stalematey TF2 is a result of the way TF2's classes and their mechanics are designed, as well as how the community has designed 6v6. If we want to rid stalemates from 6v6, the game's mechanics and the gamemode's rules need to be designed in such a way where the chances of pushing successfully outweigh those of holding successfully.