I can't help with booking, but according to the Skyteam website, you're only routing options, one-stop, on Skyteam, are via CDG and FCO. Can you get to BEY? There's a non-stop on MEA. I can find availability via AF/KL, in Y for 15K Flying Blue points, but on DL only J for 40K Skymiles. For the one-stop, I can find availability on AF/KL for 34,250 Flying Blue points, via FCO, but I can't on DL. I get a weird Miles+Cash error message in the app when trying to pull up the same days. Good luck.
https://applications.skyteam.com/rou...stinations/TLV