Yes, eating time is included in A time.
Have you tried going into his nursery about 20 mins into his nap and putting your hands on him, gently, so that you can try to 'ease' him past that wake up? That's the first thing I would try. I'd be sure there's no external noise waking him (doesn't necessarily need to be happening 30 mins in the nap, but if it's ongoing and he's in light sleep at that time) so maybe some white noise. Is he swaddled? Is his nursery really, really dark?
Don't worry about PUPD. It is fine to pick up if he is crying, but try to settle him in his crib first. I would shush-pat for 20 mins or so to extend a nap, but if he's not settling then abandon the nap and bring the next nap forwards.
I never had any luck with patting on my LOs chest/shoulder. I used tightly rolled receiving blankets to wedge him on his side, and patted from there.
No need to wake at 7, if his days go better with a later morning. Enjoy the lie in!