Don't shake them. Don't worry about the bulk priming because how, logically, can that be a cause of the undercarbonation? You added plenty of sugar to do the job. There is always enough yeast in solution, even in clear beer, to do the job. So until you have eliminated temperature as the cause, then that is what you have to go on. Given that we are pretty sure that the problem is one of temperature, and given that yeast work better the younger they are, then I would certainly be bringing all your bottles inside (and monitoring the temperature) for a couple of weeks. It is a process of elimination. If that simple solution doesn't work, then and only then should you worry about other causes and possible remedies.