Those living near or in a hub will usually be worse off in Miles and More and for pricing but your best bet is going to the Balkans (Ljubljana, Split, Dubrovnik, Tirana etc.) or Athens and then connecting once or twice via Munich, Geneva or Vienna and then onwards to Frankfurt, Zurich or Brussels then further on to Tel Aviv for around 5xx to 6xx €.
Similarly, Beirut pops up from time to time with a decent fare when it is being run (mind the visa on arrival if you do enter the country, it is very cheap however)

Finally, slightly more expensive but safer is Amman - mind the visa on arrival for Jordan compared to Israel's ETA, this one is a little pricey - with Split and Athens the best starting points here and consistently able to show fares with 2 connections in the 6xx € range.

Another option for you is to go during the Winter Schedule or in the Spring (only for UAE) to the Middle East with Eurowings from either Berlin, Hamburg, Düsseldorf, Cologne, Hanover, Nuremberg, Prague, Stockholm or in your case Stuttgart.
If you can find a cheap way to position yourself to any of these airports, there are fares for even direct turnarounds in the high 4xx to 6xx range for 400 P/QP/HON depending on the dates and how far ahead you are booking, they are great to start the year or garner the final remaining points necessary.

As a Swiss citizen, Lebanon, Saudi Arabia and Jordan are all Visa on Arrival or eVisa, ETA for Israel and visa free for UAE, same as Germany.
Keep that in mind for added costs.
Israel and Lebanon are cheap while Jordan is decently pricey and Saudi is very expensive for a visa.

As long as the spend doesn't exceed 3 € / CHF per QP/HON it is an okay deal usually but anything intercontinental you can keep under 2 is fantastic.

Edit: Pretty much in all sweetspot destinations in the Middle East a direct turnaround can be done though not without some stress.