You've received some great advice from many people
. I do have a few thoughts and questions.
The stirring during the night might be gas and might be because of the DF, but could also be routine related. The waking at 6 is perfectly fine, but him playing after it in his cot makes me think that there is something off with his A time and his naps.
Consistency is generally very important when using EASY and BW, and very very important with A times. Most babies would have a similar A time throughout their day. Some prefer their first A shorter, some longer, some prefer their last A short and some long, but it would all pretty much be around the same length.
At 12 weeks you are looking at something between 1:15h and 2h (which would be a high A time needs baby). IIWY I would make my priority figuring out his appropriate A time. I would start with 1.5h A time ans stick to that throughout the day and no matter what. He might seem ready for his nap before but you'd need to be strong and think that in this case you know better than him what he needs. After doing the 1.5h A time for 3 days we can look at your logs and try to make some conclusions out of it.
Prepare yourself for getting short naps - it's all normal.
I must also say that I think your mid day long nap is contributing to the issues you are experiencing. I don't have Tracey's book next to me but she talks there how day sleep should be limited as well because it can steal from night sleep.
It sounds to me as if he doesn't really know yet how to fall asleep independently, am I right? If so then parallel to working on his A times I would work on teaching him how to be more independent sleeper. The best way to do that in this age is to have a proper WD (more about it here:
What does a good wind down consist of (Includes 4S ritual)) and to use Shush-pat (more about it here:
Shush-pat - How to). A baby who is dependent on a parent or a prop to fall asleep will not know how to settle back to sleep when waking up at night and early from naps, no matter how tired he is.
Consistency is key here as well - you need to do the same thing for every sleep so he has enough signs that sleepy time is coming. If you put him for one nap in the car seat, another nap in his crib and another in your bed (just as example) then he won't know where is his sleeping space. If for one nap you feed to sleep, for another you are rocking and for another nap you pop him in a sling - it's all going to be confusing for him. Babies need consistency.
I think you get my point, just do the same thing for every sleep so he can learn.
Like Kara said, try and offer 5-6oz at night even if you see that he is not drinking all. You always offer more than baby actually takes so he has the possibility to take as much as he needs. If he is draining bottles then it's a sign to increase the bottle volume again. The slow drinking can be either a slow teat or that he is not hungry enough. At this age I would space his feeds at least 3h and not offer a bottle in between because he will just snack and of course - use a faster teat which you say you already do.
HTH some.