So I generally agree with the others that checking your bags all the way through likely will be fine, but if a lost or delayed bag really would be a "disaster," than it seems to me that you shouldn't risk checking your bag at all. Whether your connection is one hour, three hours or 12 hours, some bags misconnect (and of course there is a risk, albeit smaller, that your bag won't even make it on the LAX-JFK flight).