Just to round it all up ... we're flying out shortly, which means leaving on Shabbat. We thought the safest option given the OMG o'clock flight would be to arrange the taxi via concierge yesterday, as you can't always rely on using an app especially on a day when you're not sure how many taxis will be on the road. I was expecting 150-180 NIS based on research, but quoted 200. Fine, all good and booked. 15 minutes past the departure time....... still no sign of the car at the hotel, so the chap on the front desk just booked one using the Yango app (could have used the Gett app also - that showed about 10 cars around and a <4 minute wait too) and rocked up a few minutes later, only 150 NIS. I would just go for that option, seems pretty reliable.
@Pushka if you're heading via LON prior to going on your cruise then I have some cold hard NIS if you want a little slush fund prior to arrival
The trip all went off without any issues, I wouldn't hesitate to recommend DIY for these 3 countries (Israel, Palestine, Jordan).
If anyone wants to know anything else or has any questions, just shout.