In my experience, the training is totally unnecessary and it's 100% about food intake. Even friends I know who successfully "trained" were able to do so because the babies weren't hungry at night. Babies often seem fine and satisfied druing the day, but could actually eat more, thus the reason they wake at night.
4 1/2 months is old enough to sleep through (just barely). My aunt, mother of ten, got all hers to sleep through in their own beds at 3 months, but they have to be FULL. This is tricky at 4 months, especially if you exclusively nurse and have a big hungry baby. Sometimes they simply NEED to nurse at night still, due to hunger, not security.
All your baby needs to be is FULL to full capacity (different for different kids) and then if you don't mess with them at night, they either A) self sooth or B) don't wake up to begin with.
Feed him more all day long, not just right before bed, offer more food more food more food. Once he has had a calorie increase for three whole days (takes a few days for body to register it) you can walk away at night and never go back. This worked with all of mine, but my 2nd and 3rd were still hungry at night until about 6 months because I was just nursing. That was my choice, so I fed them during the night for as long as I chose to nurse exclusively. But once I supplemented some formula and thickened bottles and added some food, boom, they were out all night.
Your little guy sounds hungry to me. I never allowed more crying than just a few minutes when they were first put down, and a little if they woke but I KNEW they were full. Otherwise I fed them. A hungry baby will not self sooth.
ps, I love Dr Sears vaccine info, but some of his attachment parenting theories are dead wrong, not so much that they might not be great ideas for some people, but many of his claims that other styles are damaging are wrong -proven by generations and millions of healthy babies. I cant' believe he gets away with some of his claims. Generations of self soothing CIO humans with no damage whatsoever are evidence of that. Don't let anyone tell you his word is indisputable scientific fact, it's very disputable. Respectfully to Jodi, kids not manipulating until age three? That's totally inaccurate crazy talk. Many different experts will back that up. I'm saying that from the heart and sorry to cross a boundary.