Hi,
for new rings and/or barrel, gentle the first 500-700mls, then change oil+filter and take no more pardons.
I use Castrol 10W/50 RS4T in the street bikes. It is a so-called motorcycle oil supposedly better able to deal with the wet clutch. I have also used RS 10W/60 which is an auto oil with no disadvantages for the clutch or cam plain bearings that I could tell.
In the Skorpion SOS racer I use Castrol Formula RS 0W/40, an auto oil but I have no problems with the clutch and none (yet!) with the motor.
In the Bimota DB1 I use the RS4T as well. It has a dry clutch of course so it wouldn't much matter; I use what I have on stock.
In the Laverda and Mondial I use Motul 3000 4T which is a pure mineral oil. The Mondial has a 13 plate all-metal clutch whcih does not work with more modern stuff. And the clutch in the Laverda is 20 years old and I don't want to risk washing it out with synthetic stuff.
Is the bottom of the airbox dry? It can't be really. That is where the oil ends up as a rule. Some motors just blow it out big-time; a few don't blow at all. Depends on rev-range and crankcase vent, too. My '94 Tour has always blown oil out. It is only a problem with prolonged expressway driving at 85mph or more. Backroads with intermittant revving to the limit creates no problems. The '96 SZR and the '95 red Skorpion Sport are practically dry, in the case of the Sport even at prolonged (200km+) expressway driving at 110mph (true electronically measured speed at 8000rpm). The racer engine has always used a little bit, still does but a bit more but then it gets revved to over 9000 at times. Look at the vent on an OVER racing engine: it is at least 2" dia. not the 1/2" hose on the stock engine.
My racer has a second 1" vent on the cylinderhead.
Of course if you use the xtz engine as it was intended (around 4500, always below 6) there is no problem at all with that tiny vent. But to get an idea, take off the seat and watch the oil tank blow up it cheeks with each stroke at slow idle. Most 50s bikes (and older) have a one-way valve in the vent that closes under pressure; oil is not throw out but it does use some performance since the piston is going down on an air cushion. Racing engines then had only a long hose out the back instead. Or two. My Motobi has the long hose and two! additional vents on either side of the rockerarm cover.