You must only do what you feel is right and what you are comfortable with, regardless of what anyone says here or IRL. You are his mummy, only you know him best (here it is just words and numbers!) and only you have your mummy instinct for your LO.
Tracy's methods are not free of crying (or screaming) however they are vastly different to controlled crying or CIO as you never leave your baby to cry alone (this means there stress hormone is either very low or not detected). Do try not to feel guilty about your LOs crying or sleep, you can only set the scene for sleep you cannot force it to happen, and as much as he cries so long as you are there he knows he is safe and not abandoned.
In TBWSAYP Tracy describes a baby of almost 4 months old being transitioned to a 4hr EASY. As the mother begins to sleep train her baby and he wakes after 45 mins they continue to try to resettle him for an hour, it is then close to his feed time so they stop trying to resettle and continue with low key activity for the rest of what should be nap time, then feed, then continue with activity until the next nap time 2hrs later, he doesn't settle at that nap time and it takes an additional 45 mins to get him to sleep (A time now 2hrs 45) and when he nods off Tracy tells Mum to wake him 45 mins later because he has used up much of his nap time being settled to sleep and Tracy says the goal is to get him on a healthy sleep routine. This baby was almost 4 months. (see page 232, 233)
Now I am not saying you should be this strict about naps times, often on the forums we have a much slower/gentler approach to sleep training, in part at least because it is such hard work on the parents. I just show you this as example of how hard an A time can be pushed when Tracy did not consider it a problem at all, in fact it was what she was telling the mum to do. Although Tracy warned us of letting our LOs become OT she was not against OT during sleep training to get a good routine going.
Short naps in this age range are described by Tracy as having come from either lack of routine or not moving up to the 4hr EASY when the window opened. Honestly so so many of us have gone through it. It's what brought me to the forums. Just looking at your EASY I am wondering if there is a reason he is not fully moved to a 4 hrly E and if there is reason for the cluster feeding in the evening. it looks like you partly moved towards the 4hr EASY but didn't fully make it there. It's ok if there is a reason (mine had to have 3hrly feeds due to reflux until he was 6 months old), just checking that you are aware of it yk?
Were those 30 min naps at home or out and about? Did you watch the nap to see what happened? What are you doing to resettle after a short nap now? How long did you try to resettle for? Are you trying w2s to shush/pat him through his transition? sorry for so many questions just trying to get a handle on what's going on there for you.
The 2hr nap in place of the CN, I wouldn't let that become a habit. Yes it sounds like he crashed out to catch up on his sleep but you don't want it at 3pm, a long nap then can start to disrupt bed time, he really needs to get that nap earlier on.
More hugs for you. I know this is not easy, I've been there. It is exhausting, worrying, guilt-filled...
This will pass, it will x