1968 GTS 340 with Carter AVS 4966S

Sounds like a good plan.
After this I will reassamble everything and meantime use some radiator sealant to prevent from leaking again.
I would be cautious about this. Use a product that can easily be cleaned out so it will not cause problems during soldering.
Old timers will use ground pepper to seal minor leaks.
The leak sealer used by GM on some of their problem engines has ginger and similar ground products.
upload_2021-6-18_8-36-49.pngupload_2021-6-18_8-37-28.png

Talks with the shop that will be recoring. These seem safe but they'll know from experience if some cause problems for their work.

I already figured out that we have Prestone also here in Austria, so I am going to use it for a complete cooling system flush.
OK. Just don't use Prestone's coolant as , at least in the US, they only offer a HOAT. Find a IAT. Around me, the easiset way to buy a conventional IAT coolant is the store branded stuff at Autozone. Everything else is "universal". :(

Then I will set the timing and adjust the carb and then recore the radiator.
Once its running, measure the timing at rpm from as slow as you can run it, and then at increasing rpm.
Then we can figure out what the initial ought to be.

Now again some questions:
I am not yet sure about the fan clutch. A non thermal might be correct for my car, might also be a thermal one (I will probably know for sure when I get my repair manual but I would like to order the fan clutch along with the repair manual). Is there any problem if I just get a thermal clutch since I think that they work a little better than the non-thermal ones?
I don't see a problem in concept.
The challenge will be in execution.
Critical will be the spacing of the clutch. You will need to find measurements of an original fan clutch for a 1967-69 small block (273/318/340). Then you can compare with the spacing of the various aftermarket replacement fan clutches. You would think they would make replacements with exactly the same dimensions. Do not count on it. They may, or they may just sell one that is 'close enough' in their opinion.
You will also need the matching fan. Those are relatively easy to find used. The part number is often still on the fan so sellers know what they are.
Finally you will need different attaching bolts for clutch to the water pump and the fan to the clutch. I'm assuming Unified (US) standard hardware may be more difficult to obtain in Austria than in US.
(Unfortunately I have a later engine and water pump in my '67 so can not offer the dimensions you'll need)

And do I need a fan clutch wrench for the replacement?
I've never used one.

When you have a look to my first picture of the complete engine you will notice that there is the by-pass hose installed but the other one going from the water pump should go to the heater box. In my case it goes directly to the engine where the hose coming back from the heater box should be.
Classic method of elimating a heater leak , or eliminating a heater completely. LOL.


You may find this 1968 Master Tech booklet Engine Temperature Control answers many of your questions.
https://www.mymopar.com/downloads/mtsc/251.pdf

A fairly complete list of the Master Tech series is here
Master Technician Service Conference - Chrysler's Training for Mechanics

Unfortunately that web page's links are somewhat of a mess right now.
So until that is fixed, use the above page as an index, and then go here to find the filmstrip/movie or booklet in pdf format.
Chrysler Master Tech Service Library – Browse Model Year – MyMopar