I view PTP as being heavily-vehicle focused- camping requires everyone driving to particular spots and driving itself is a strategy. A lot of the game is sacrificing yourself to help your team, even if you aren't where all the action is happening. The whole thing is focused around where the President is and what he's doing. This is what distinguishes it from a shitty TDM.
Your "maps" are so small that vehicles aren't even an option, and there could only really be one spawn point for protectors and one for attackers. The President would basically have to sit in a small corner of the map to avoid getting killed while the two sides pointlessly duke it out in the center of the map. Does this sound like PTP to you? If it does, we have a problem.
Keep thinking about it. What do you do with the civilians? Do you just find another corner to spawn them in? What purpose does the President even have, if the map is so small that he can't avoid fighting? He'd just be a special prize for the terrorists to kill.
I'm not sure I even understand the problem here. If the maps are lasting too long, you have the power to change that. Be a terrorist and kill the President and VP, or better yet, be the President and end the map in 15 minutes. It's the basic idea of the game. If you don't understand this, I have a feeling that you spend most of your time camping at the armor spawns and ignoring the GM.