I used this book and I think you can use it anytime, because it isn't really sleep training. It is more about learning why baby sleeps the way it does (or doesn't) so you can make sleeping more likely to happen, and partly about training yourself.
Some highlights-
Consistent routine. This will be hard with moving and such, but very important to do your best. Do the same sleep routine at the same time every night. Bath, bottle, book, rock, bed. Or whatever you need to do. But an actual routine is important to let them know what is coming next. (bath didn't work for me, it always made him hyper).
Low lighting and calm atmosphere at bedtime. After dinner, dim the lights. Close the drapes. Keep things mellow. Rowdy play to tire them out wont work.
No tv- the flickering lights makes them hyper.
Early bedtime instead of later. Moving bedtime up in 15 minute increments until you find a time that works. When it is right, baby should be easier to put to sleep and should sleep longer. If they are over tired, they sleep worse. The same as when we are so exhausted that we are "too tired to sleep".
Getting baby to fall asleep on his own is essential to getting him to sleep through the night. He needs to self soothe so that when he wakes up a little, he can put himself back to sleep. So rock him or snuggle or whatever, but then put him in his crib. I can't really remember what you are supposed to do if they cry, you might want to read that section. It had to do with soothing them by patting talking softly and stuff but not picking up. Then not talking anymore. Then just being close, etc.
Give him a pacifier or a lovey or something to help him soothe himself. Put a lullaby cd on repeat in the bedroom, or use a white noise machine. Use a nightlight.
Use a "transition to sleep" phrase. When you are done with the bottle, book and rocking, tell him something like "Okay it is time for night night now. Mommy loves you." Start doing this along with the routine immediately. Get him used to hearing that cue and learning that it means sleep time. I started my son by still rocking him to sleep and saying this as he was dozing. Then after a few days, I said it right before he was going to doze off. Then moving it up a little bit at at time, until I said it as I was putting him in his crib. Eventually, you will be able to use the phrase as part of your soothing-but-not-picking-up technique. The book described being able to say it from the doorway when they heard baby starting to truly wake up but before the crying started and baby would go back to sleep. (kinda like pavlov's dogs).
I can't remember the whole "method" but all the point was that there wasn't really a method the same way as CIO. Doing those things like the sleep phrase and a routine immediately will get him ready. Then in a few days, start moving bedtime up. Then when you think you have the bedtime right, start on getting him to fall asleep on his own by shortening the rocking time each night. Hopefully one night soon he will roll over and go to sleep on his own. If you co-sleep, that is fine, but put him to bed on his own and leave the room. Don't feel bad about co-sleeping if that is what you have to do to get some sleep. You will have to deal with the sleep issues later, but maybe things will be more settled then. Consistency is the key though. No matter what your sleeping arrangement is, stick to the same thing. Don't try CIO then give in and go get him. Then do it again when you are exhausted. Then bring him in your bed, but the next night put him in a crib. Doing that will make sleep training impossible. Pick a routine and stick to it, no matter what your arrangements are. From all your posts your son sounds a lot like mine. He will sleep one day I promise. Don't be surprised if he totally regresses and you have to start over after a move or teething though. No matter what method you use, this will happen. It is not a one time fix.
Sorry this is so long, I tried to condense as much as possible. If I didn't explain something clearly, email me. Good luck!
Added- Oh yeah, naps. He needs naps to be able to sleep at night. No naps equals overtired babies who can't sleep. Naptime should also have a routine. Same time every day more or less, but watch for sleepy cues- rubbing eyes, crankiness, etc. He should have a nap in the morning and a nap in the afternoon. A few hours after waking up- mine woke at like 830, so naptime was 1130. And then second nap was at 2 or 3ish. (And watching for those sleepy cues at night will help you pick your bedtime better too.) I fed my son and read a book to him at naptime too. Rocked a little and then put him in his bed. I started the sleep training later than you, so it will be a little different than what I did. Use your sleep phrase. Getting blackout shades will help too, mine didn't like to fall asleep in the daylight. They sell them at Target now.
One thing I have heard is to not make bottle the last thing they do before sleep. Don't let them fall asleep with the bottle, because they will need to have it to fall back asleep. So make it an early part of the routine. Fill his tummy, but then do the books or singing lullabies and snuggle time afterwards. Make sure drinking a bottle isn't the cue to fall asleep. Getting your whole day on a routine as best as possible will help with the sleep. Make it about waking up, eating, then playing, then sleeping, repeat. You don't have to schedule play if you don't want to ( I didn't) but nap and meal times should be consistent. If baby is showing sleepiness it is okay to speed up the routine, like reading one book instead of two, or shortening bath time. Getting them to bed before they hit that second wind is important.