Great question — answering as the UphillTech team:
In theory there is nothing wrong with what you are attempting. But in practice there might be troubles. Assuming that you are a citizen of a VWP-eligible country then there is nothing in law stopping you from using the VWP very soon after the end of your J1 visa period. However every entry under the VWP (or even with a visa) is at the discretion of the border guard when you enter. One of the requirements of the VWP is not you not use it "to live in the US through repeated visits". It could be construed by a border guard that you were attempting to extend you time in the States unfairly after the expiry of your visa. If they thought that they could easily refuse you entry, or worse. The...
Full answer by DJClayworth: https://travel.stackexchange.com/a/194574 (CC BY-SA 4.0).
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