So two things - first of all, he would still need more A time. 3h is not enough at his age, so I would work on increasing that by 10-15min for the next 3-4 days and then we'll see how his naps are.
The NW can either be because of UT but can also be because the bottle became a prop and he is dependent on that now to settle back to sleep. You have two options. The first one is to go "cold turkey" on all or most NF (you can still leave one in the middle of the night for now). Every other NW which is not at the time of NF you chose you are settling with PU/PD. I know you said it makes things worse, which is what most parents say, but if you stick to it for 2-3 nights and do it the right way then you will see a change already in such a shirt time. But you gotta put the work, yk? Here is some info:
How to PU/PD (inc age adaptations)The reason why most parents think it's worse with PU/PD is because there is a lot of crying in the first night, but if you go through that night then things get better.
The other possibility is to go gradually with the bottle, so increasing the volume of it by an oz every 3 nights.
Good luck!