Unless you have the patience of Job or are experienced in dealing with El Al, I'd recommend you find a TA in NYC that has an excellent relationship with El Al (and there are these TAs in NYC - Israel specialists) who can research and book a business-class RTW using El Al's and Qantas' joint RTW product.

You have to fly El Al over the Atlantic and Qantas over the Pacific, but your route would easily fit into that product, and the published price ex-USA is under $5000, v. $9100 for the standard Oneworld product (both plus taxes and fees.) Obviously since with the "QFLY" product you can only use El Al, Qantas (and I believe Air Pacific, the Fijian airline) your routing options are fewer than with the OW RTW products, but your route would work.

You have to book with the first over-water carrier, so in your case that would be El Al. I tried doing so a year or two ago, and found that nobody at El Al (a) knew of the product, and (b) was interested in the least in learning about it. Qantas, on the other hand, had no problem booking it, but that was going in the wrong direction for me. That's why I'd recommend the travel agent route - somebody that does a lot of business with El Al and has the patience to work through their "marketing" (oy) methods.

Otherwise, you'd need to modify your route to something like JFK-LHR-TLV-LHR-HKG... which is no bid deal, albeit around $4000 more than the alternative.