I agree with the PP - a lo will tend to wake up more in the night when they are over tired and it can turn into a vicious circle. Defintiel agree, the stoller is a fantastic idea - the fresh air does them the world of good.
Also to try and cut down on the feeds during the night, have you thought about trying to do a cluster feed at all? You could do the first cluster feed after he has woken from his cat nap, then you can do the bath as your A time, and then do a second cluster feed again after the bath then your wind down routine and then bed. This will tank your lo up and will probably enable him to stay asleep for the dreamfeed.
At 12 weeks it is still quite common for them to wake for a feed in the middle of the night.
HTH
Paula x