I would go over to the HONDA forum here on HUBB. Start a Trans Alp thread, or find on older Trans Alp thread already there. LOTS of hubbers have done long trips on the Trans Alp ... LOTS of good knowledge here ... you just have to ASK!
Also, there must be a Trans Alp Forum in Germany? Ya Ya?
I don't know the bike well myself, but I do know basic carburetor function.
Is it just ONE Carb or two on your bike? I'm guessing TWO Carbs, one for each cylinder, ya?
One is easy. But both your Carbs most likely will have TWO adjustments.
One is the Idle adjustment. I'm sure you have found that one by now? One Screw may adjust BOTH carbs at once.
The other will be the Fuel/Mixture screw. (each Carb has it's own)
The 3rd element that can affect idle is your choke (enricher) Make sure it's working correctly and not STICKING ON. This happens on older bikes. Use WD40 or similar to free up choke cable and operation.
It is normal for idle to SLOW DOWN once you shut OFF Choke. Choke should only be used for starting engine. Once engine is running for less than 5 minutes ... turn OFF choke. Idle will drop down slower. This is normal.
Fuel Screws need to be adjusted correctly as well. But first, set idle with
Idle Adjustment screw:
Ride bike until fully warm (HOT!). Put in neutral and note Idle RPM number.
Make sure Choke is OFF. (closed)
I would set the idle between 1200 to 1400 rpm. (this is your choice! I prefer a slightly higher idle!)
If two carbs, then carbs must be "in sync" then adjusted individually.
Read up on your Carb(s), learn about the Fuel/air screw, sometimes incorrectly called Air Screw. It actually controls Fuel flow at very low RPM,
like Closed throttle up to 1/4 throttle . You generally adjust the Fuel screw to obtain the highest idle (also do when engine fully HOT)
Turn adjuster screw OUT until highest/smoothest idle is found. Now, screw adjuster IN on half turn. (more lean) You're done. For best fuel economy always run this setting as LEAN as possible and still maintain a smooth idle.
Once that is done ... re-check Idle adjustment and put it back to 1400 RPM.