Hello Gerhard! Sorry to hear about the oil usage.

The top end rebuild does seem best. Valve seals seem a good idea if the engine is otherwise running fine. I cannot imagine anything in the lower end (crankcase) that would use oil as you describe - without leaving a puddle while parked!

My main focus has been electrical on my project, but the engine startup is coming very soon.

I believe we discussed this previously, but are the spark plug deposits looking normal?

Now for rebuild parts, I believe the MRCycles link off the main GSTwin page does international shipping. Here is a link to their 1991 GS fiche. You can find your way around to the other years if needed.

Try using 20W50 oil.

My counter is currently 63000Km, and oil consumption is
something I'm concerned too.

I used Mobil 1 5W50 once, and got a consumption like yours.

Now I use Castrol 20W50 and consumption is around 150ml
per tank... that is 1litre per 1000Km (0.2 gallon per 700 miles aprox)

Shouldn't you be measuring the clearances for the pistons before you decide to replace them? Also the ring gaps and thicknesses? The oil problem is much more likely to be valve guide seals than rings, but only measuring everything can truly reveal.

I agree.  More likely that it's in the head but here's how you can tell for sure - maybe you don't need a total rebuild.

Test compression in the morning after the bike has set for a while.  Note the readings, then squirt oil into the cylinders and test again.  If there is a significant difference then I would continue looking at bore/newpistons etc.  If the compression is good to begin with (dry test) then the head is the culprit.  The smoke at startup is an indicator that the valve seals are gone, which means a valve job is probably needed as the guide-to-stem clearance is probably worn too.  

Now 150psi...  now that I think about it..... is it 150 on both?  or 150 and 190 or something like that?

heavy oil use with good compression and only minor smoking tells me valve guides and seals, specialy if the smoking stops once warmed up.

The compression is 150psi on each cylinder (so they're the same)
As you can see from my other thread I've decided to first do the head and then see what happens. From what I understand this bike should be able to do much more miles on the same set of rings and that compression is still within spec.