Hello Brazylia,
Sorry things are not going well with your LO
All the above advice is good in my opinion.
The only thing I might add is that if he's falling asleep in your lap during the book reading, I would try to put him to bed earlier, because I think that babies that fall asleep on their own tend to sleep better, and need less props to get back to sleep, etc. I imagine that him falling asleep that way must have been a nice break for you though, after going through all that PD!!
Naptimes earlier, and bedtime earlier : this is what worked for us!
When she wakes at night she is awake less long now. (lucky, I know!)
We keep the activities to a minimum as of 5 pm. We don't let her get even a glimpse of the tv if someone is watching it, and we keep her 5 year old brother from jumping and being his usual energy bomb around her
And as hard as this one is, we don't make her laugh after 5pm. We've noticed a BIG difference when there's a 2 hour 'calm' period before bed.
As my husband keeps repeating to me, 'good sleep begets good sleep', so I would try to work on his naps and bedtime hour.
Good luck and keep us posted! xx