Hang in there! You're doing great and so is your lo!! Don't worry there will be set backs. It is not unusual for the baby to resist after initially accepting. It is also not unusual for the baby to cry to the point of exhaustion, but remember you are with him.
Your wind down for night sounds great. Tracy does say to keep swaddling as long as possible, however, I did also abandon it early because my dd simply wanted to be sprawled out. You can also try a sleep sack or bag. It provides a snug feeling but the baby can still move around.
Since you are breastfeeding he probably still needs that 3 am feed. Look towards 4 months for ending that feed. What does he weigh? After you get pat/shush in place you can experiment with ending it- e.g. by trying to pat/shush him back to sleep at that time, but I'd hold off for a bit why you are sleep training.
Do you have a wind down for naps? Something that you do before every nap is great but is also different from the bed time routine. For the naps you did great not giving in until the next feed but try to keep him in his crib- you can pick him up if he is hysterical and pat/shush on your shoulder- but when calm lay him back down. For naps keep going until the next feed.
I know the crying is so hard! Please know that he just crying because he doesn't understand, he is frustrated and it is different from what he is used to. you are not hurting him, you are giving him the skills to sleep independently in the future
Also- yes, do not go in at first peep- wait to see if he will resettle. If the cry escalates go in but give him a few minutes. Babies often wake at the 45 min mark but put themselves back to sleep in 5 to 10 min. Mom's rush in- oh boy I did- and startle the baby who was sort of still asleep :? Let him do his thing but go in when your mommy instincts kick in.