hi,
i think it's kinda your personal preference, and you work with the natural tendencies of the child. both my kids did their first long stretch from 11pm-7am or 10pm-6am (around 3 months old, so a bit older than your little one), and i was able to slowly bring it earlier & earlier.
keep in mind too that there is a growth spurt around 6 weeks old - that might be why he is a little unsettled now too.
HTH