File B1 extension or COS to H1 and by when?

[eb3toeb2user]

Currently in US on B1 stay valid till Jan week 1. Also have an approved H1B notice. But yet to close a suitable job so haven't yet filed change of status to H1B. 

 

Question - how long before current I-94 end date, should I file either a B1 extension (reason - extension of business visit due to extended project) or a change of status to H1?

 

I read on USCIS that if I file either B1 extension or H1 COS even few days before I-94 expiry, I can stay up to 240 days after the expiry, pending the approval.