Hi and welcome to the forums
First off, I want you to know you're not the only one that battles with short naps. You're not doing anything wrong. I battled for ages with DD too until I found this site.
This link is a really good one to keep handy
Average A times- BOOKMARK ME! Unfortunately short napping at this age could be purely developmental and anything we do to tweak can't really help until the developmental phase is over. They are just becoming more aware of the world at this age, and probably think sleep is for the weak
I totally admire your resilience with the ssh/pat, and it does show that it works in that it gets him back to sleep but tbh I wouldn't just for your sanity hun. I'd go with 15mins max, after that, give up and get him up and do some low-key A, reduce the next A time slightly by 10 mins or so and try again for the next nap.
I think he might be getting a little OT as the day goes on. As you can see from the link above many LO's are averaging around 1hr 20ish A time. How do you feel about actually reducing that first A time a little and trying for a nap after 1hr 20 A? You could give it a go and see if it helps?
Now I might be completely wrong and that he actually need more A time than is the average, but thought we'd try this out first and see ok? I think it's best to rule out any chance of OT in case we make matters worse and start extending the A.
How does he wake during the naps? Is he upset? Do you think it looks like he needs more sleep or is he in generally good spirits? I presuming the former option since you try so hard to get him back to sleep?
Do remember E is part of the A time.. S is calculated from eyes open to eyes shut, everything else is A xx