Some capt. I fly with, actually insist that on an offset non-precison you should fly to the MAPt and thereafter position yourself on the runway track. In my opinion this increases the risk in having an unstable approach, but sometimes the offset is on purpose to avoid an obstacle on the extended centerline...
Actually, the offset (resulting from the offset location of the VOR or NDB - not on the CL) is to ensure that the approach track passes through the centreline at some point, at or near the MDA so you only need to do one slight turn to get lined up. Otherwise you would be left, at the MDA, with a double turn to get lined up. It's the nature of the beast that you may not be "lined up" with the runway by 500ft AAL during these types of approaches. Your stabilised Approach criteria should take this into account.
AS to when, in the JFK case, you could turn right to pick up the CL if visual, I'd say, why bother? Just fly the approach as published, and when getting close to the CL ie approaching the MDA, turn left the 9° and land.