I have heard the same thing that you need at least 2-3 paystubs from your company... (but I would recommend you talking to the lawyer on that.. many people have different opinion) but there is an alternate way... Since you already fall within the quota of this years cap.. You can file for another H1 through the new company because you can work for multiple companys under multiple H1s.. So you can get them to sponsor for a new H1 which won't be a problem as you have already got accepted once you get the H1 for the new company you can just go ahead and leave the old company...