Infant sleep routine help

We are really struggling with our nap/bedtime routine for our three month old. It seems that he has learned that this sequence of events means sleep, and he wants nothing to do with it. When we start our sleep routine he becomes upset and cries/screams inconsolably.

Background: He is an great sleeper at night, typically sleeps from 9:30-8:30 with two feeds (one at 11:30 that we wake him for because of a medication and once around 5 or 6). During the day he is awake 1.5-2 hours at a time and takes about 4 naps. He’s been struggling with length of naps lately, but that’s a separate issue.

When I notice he is becoming tired, but before he gets fussy, we start his sleep routine which includes: dim room, diaper change, sleep sack, pacifier, sound machine, book, snuggles in the rocking chair. Before bedtime at night we also try to do either bath, quiet playtime in the nursery or infant massage leading up to this. Lately, once he realizes what’s happening, all bets are off and he just LOSES IT. This is even impacting other parts of our day (for example, when I read a book during awake playtime, he is getting upset because he thinks it’s related to going to sleep).

Other things:

He is breast fed about every three hours and feeds are not tied to him going to sleep. If it’s time to eat, I feed him as part of this routine, if it’s not, I don’t. We are hoping not to get stuck on him needing to nurse to sleep.

He does pretty well self soothing and can put himself back to sleep through the night when he wakes up. This is less reliable during the day, but we’re working on it.

We are not comfortable with a cry it out sleep training plan (personal decision, don’t come at me)

I’m at a loss and need suggestions for how to make him enjoy and calm with this sleep routine instead of it having the opposite effect. Oh, how I miss the days where my baby was happy to snuggle when he was tired.