Thank you for a decent constructive non-aggressive question - bookworm
The dep was ALGOI 1W so initial heading was 240.
I have tried to contact both Zurich and EDNY ATC by phone to ask what their usual procedures are, but without success. I got Zurich but not the area controllers. Of course I know one flies the SID and climbs as instructed ON THE SID, or to the SID's max level if specified (in this case it is 5000ft) if no level is given.
The contact was transferred to Zurich well before I reached the 4D mark i.e. well before the left turn on the SID.
My suspicion is that when Zurich gave me the climb instruction they said something else like "continue" and I took that as "continue heading" and read it back accordingly, slowly and clearly as I always do, and the absence of a query on an otherwise non-busy channel seemed to confirm this was either OK with them, or they would have given me some similar heading anyway so they let it go. They weren't busy so they could have yelled at me very easily. Anyway, that's what readbacks are for, to pick up mistakes.