i'm pretty sure around 4 months is a horrible time for sleep - there's lots out there on dr google about '4 month sleep regression'. could be a wonder week or growth spurt as well.

how did he sleep after you gave him the second bottle the other night? maybe give him a feed at 10.30 or 11.30, even if just a small-ish one?

i think he's still awfully young for self-settling. the only books i've really read are pinky mckay books & the no cry sleep solution as i could never bear to let my DS cry either. the pinky books didn't really give me lots of ideas but did reaffirm to me that i was doing what felt right.

ETA - i BF so i know it's different but my DS was feeding every 2 hours around the clock still at 4.5 months so maybe he is needing a bit extra?