One option, as suggested by javabytes, is to get an Israeli SIM and forward there.

You can get through Annatel and it includes a virtual American number. You then forward your Verizon number to the virtual American number for free instead of the higher international rates. You can do so as well with Golan Telecom.

Further, you can get a cheaper plan with them and get a virtual American number with Localphone or Sonetel, forward your VZW phone to them, and forward them to your Israeli phone number.

The benefit of these options is they are cheaper.

All that being said, if you go the Israeli SIM route, you will be able to get Israeli SMS but not American; if you go the VZW route, you will get American SMS but Israelis can't SMS you.

Another thought is that if you are already in touch with people on your American number, might be worth it to just stay there. Many Israelis can call internationally for free (it's a much more common inclusion on cellphone plans than in the US), and if you have WhatsApp, virtually all Israelis have WhatsApp and you can call there. Even local guides will call on WhatsApp from their cellphone.