Morning A time sounds perfect from what you've said. Can you write out a couple of days - 20-40min naps literally cover the entire gamut of possibilities for short naps, so it helps to know how long A time was followed by how long the nap was.
I can imagine he would be pretty OT if he's up for 1:45 A time after a short 2nd nap - makes perfect sense. Lets see if we can tweak it a bit. Shush/pat can make a baby cranky if its not appropriate - eg. if they're trying to get back to sleep themselves and you're interrupting or if they were UT for a nap and not tired enough to go back to sleep.
Hugs, these little people are puzzles!