Hello and welcome to BW forums
I'm short on time today so I may not be able to answer your questions at length but will try to give you a couple of things to try for now and then maybe we can catch up in a couple of days when I am a bit more available.
At 4 months (you're approaching) LOs tend to move to 4hr E and the A time is longer.
You can move in increments rather than a big leap.
I would add another 10 mins to your A time to see if LO can get past that 45 min wake up, being UT will mean waking after one sleep cycle.
Here's a link for guidance times:
https://babywhispererforums.com/index.php?topic=84884.0At the same time you can use the W2S (wake to sleep) method to begin to sooth your LO before the 45 min wake up which is often easier than trying to resettle after they fully wake:
https://babywhispererforums.com/index.php?topic=223809.0see naps option 1.
Here's a couple of links about moving from 3hr E to 4hr E:
https://babywhispererforums.com/index.php?topic=63161.0https://babywhispererforums.com/index.php?topic=120362.02. Am guessing I am right in waking Jack after 1 and a half hours sleep? i think he would probably sleep longer if we left him.
Sorry, I am not seeing on your EASY where he slept for 1.5hr, it could be that I am miss reading your EASY or that you always manage to get him back to sleep after that 45 min nap. If LO is sleeping you can leave him to it. 2hr nap is fine. Some do longer either because they like to sleep or to catch up from short naps earlier in the day, this is also fine but I would probably make sure LO gets E at 4 hrs so I'd probably wake him at that point or soon after (if weight gain is an issue you need to feed on time or as per health care advice butyouhaven't mentioned this).
If a nap is shorter than it should be, do you start counting awake time from the actual wake up time or do you try and stick to the S time on the routine?
You can do either. Tracy gave examples in the book of sticking to the routine to get a routine in place, this means keeping LO in the bedroom and trying to resettle until the end of nap time (or nearly) and then keeping up until the next nap time even though LO would be really tired by then as the A would be super long. This can help set a routine in place.
However, it is also okay to count the A from when LO wakes after a short nap and usually this is what you'd do after the initial period of putting the routine in place because the BW routine is not a strict timed schedule but a routine of eat activity and sleep and LOs sleep and hunger cues are used as guidance. In normal life sometimes there is something that wakes LO early and usually we'd take that into account and put down for the next nap after a reasonable A time without forcing LO to make it all the way to a "timed" nap.
Not sure about the waking after 45 min after BT, could be he needs better naps r a top up feed after bath. I'd suggest feed right before night sleep.
hope this helps