Hi, welcome to BW
Let's be frank, his routine looks great for a 7-8 month old baby. I'm amazed you can get a 1.5-2hr nap after only 3.5hr awake!
If you're going to continue with PUPD, you really have to do it for all sleeps.
Probably the very first thing that needs to happen is to abandon any plans of sleep training for the time being. Its unfair to expect a child who isn't tired to sleep. He likely seeks the breast to get back to sleep because he's not really tired enough. BTDT
What I'd suggest is getting to a routine that is appropriate for him and then if there are still issues, do some sleep training. It will be far easier and far more effective to teach him how to sleep when he actually tired.
A few questions:
How often does he miss that second nap?
Do you bring bedtime earlier those days?
You say nothing changes his night sleep but you also say you'd rather he gets the sleep he needs so it doesn't impact his night sleep. Can you clarify with perhaps some examples of how his night has been after 2 naps and after one nap?
I imagine you are exhausted! Happy to hold your hand through the process of getting your LO sleeping better.