Hi there, I've been following along and you've been getting some great advice from everyone here. I can see Anna has mentioned a twelve hour day. My DD does manage a 13 hour day usually, but if her nap is poor OR if her night sleep has been bad the night before she can usually only manage a 12 hour day. It is definitely worth a go.
It sounds like it has been hard for you recently, and I know where you're coming from as we've had very little sleep in the last month, but I do think you are getting somewhere & the best thing is to keep doing the wonderful job you are to get rid of OT and other things will fall into place more easily. What do you think about a 12 hour day?