OK sounds like morning nap is independent, or nearly, then. In that case I would try two things (focusing on that first nap, getting a decent first nap can really help the day even if you go off track on the other naps)
- increase A time a little, 15 mins may do it
Average A times- BOOKMARK ME! - do a W2S going in at 35 mins (the FAQ below says 30 min but your LO's cycle is 45 min so go in at 35) and shush/patting him right through the transition from one sleep cycle to another. This does 2 things: it can prevent him waking fully and therefore get a better sleep as you don’t need to go through the whole resettling routine which is disruptive; teaches him that this nap is longer and he should continue to sleep.
How do I address habitual wakings? (wake-to-sleep and other methods)Try the slightly longer A time and W2S for 3 days. Day 4 do not W2S but instead observe. If he wakes resettle as usual and continue W2S days 5,6,7. If he transitions on his own then we can look at the rest of the day.
Patting is not thought of as a prop because it is easily weaned. Don't worry about it for now. I'm sure you are not doing more than necessary to get him to relax and sleep. I think by the end of the day he is pretty OT so will need that help.
I would also consider getting him to bed earlier, rather than that long nap late in the day (which can mess things up, making him UT for BT even though he is overall OT from the day) leave it as a 45 min CN and get straight on with your bed time routine, bath feed etc and into bed early.
hope this helps, let us know how you get on.