(((Hugs))), it's really stressful when LOs just don't settle well. We've all been there
Please don't go the CIO route though - I can guarantee that is not an easy no-stress option and all it will teach LO is that Mummy no longer comes when he needs her
We'd love to help you out with gentler methods that maintain the bond of trust between you - if he's crying, there's a reason - sometimes it just takes a bit of figuring out
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Firstly, if he was used to nursing to sleep it makes sense that he protests much more for you than for others. Second, 8 months is a time when separation anxiety often kicks in - we had an awful time with DD at this age who despite being an independent sleeper would scream blue murder for up to an hour before settling. Are you seeing any signs of that during the daytime e.g. crying when you leave, not liking strangers?
Third - when and how do nanny and daddy put him down? Are they doing the same routine as you at the same sort of times?
My feeling would be from the routine you posted that you are trying to put him down too early, i.e. he isn't tired enough. Most 8 month olds would manage at least 3h, if not 3.5h awake before needing to sleep. I think he is probably protesting because he isn't properly tired enough to sleep, and then fighting, getting himself totally worked up and overtired in the process. Cues are all very well but can be misleading as LOs get older - for example yawns and 'zoning out' can just be boredom and needing a change of scenery.
I would be aiming for (in the first instance) a two nap routine with about 3-3.5 hours awake time between naps, and see if that suits him better and makes it easier to get him down. Say something like:
WU 6/6.30
Nap 9.30-11
Nap 2/2.30-4
BT 7.30ish
That's the ideal anyway! But worth having something to aim at and be consistent with longer A times for a few days, and see how it goes x