It's possible he was under tired (UT), but hard to guess without seeing what happened the rest of the day. If you could post what he actually does on a particular day, rather than what you're aiming for or an 'average', we might find some clues as to what might be going on. A couple of thoughts...
You seem to have missed a feed? So now you're doing 4 daytime feeds, whereas before he had 5? Or do you always top him up before BT, but you just didn't write it down? He could well be a bit hungry in the evening, considering that he's taken a bit more milk at those times recently. There's typically a growth spurt around 3mo and another around 4mo, but he could well be having one now, all babies have their own schedule!
With shh pat, you can certainly start it on your shoulder, but the idea would be to put him down before he falls completely asleep, and continue doing it in the cot. It's usually not advised to keep picking up and putting down at this age but to use shh pat (or a variation) as much as possible to calm them - as you say, it could be over stimulating to be picked up so much. With DD, I used to practically lie there in the crib with her - I mean I couldn't actually fit in there (!) but there was a time when I had both arms alongside her and my head very close, giving her as much physical reassurance as possible but with her still in the crib. You may be able to do much less than that, but whatever you do, the idea is to gradually give less help over time, until they manage to settle themselves independently.
I can really relate to how you feel about the sleeping - with DS I really struggled and thought the same as you - that surely all babies must be able to sleep as well as they seemed to in Tracy's books, and it must all be my fault that mine didn't. But Tracy couldn't cover everything in her books, she said that every baby and every situation is different, she tried hard to give us lots of tools and an ideal to aim for, but if you spend much time around these forums, you'll soon see that EASY isn't necessarily 'easy' - that's probably why most of us ended up here in the first place
On the one hand, at this age we often find that we need to use the clock more, rather than sleepy cues, which become less reliable. On the other hand, you need to find a way where you don't need to stress too much - I don't think I ever found that with DS, but with DD, I made life much easier for myself by using the sling a lot. So at this age when first teaching sleep, I only used shh pat for one nap a day and at BT. For all other naps, I had her in the sling - actually I didn't have much choice as I had to take DS to preschool and he needed a nice long time in the park or he would have gone crazy! Will your DS sleep in a sling or pram? I found that took away so much of the pressure, as I knew that even if the cot nap was bad, I could help her to catch up in the sling later, and try again the next day. I do feel it's worth persevering with BT, even if it does take a long time, as that can really affect the rest of the night, IME. So I'd suggest that you try to be really consistent with shh pat when you're aiming for a crib nap, but feel free to use props at other times, or he may end up really OT, which can cause problems. That way, you may get a little sanity back too
It is a hard stage, I think most of is here have found that, but it will pass, you will get through it and we're here for you