Welcome to the forum.
Is this a recent problem since you had the rebore done? Could it just be the result of blowby if the rings have not seated.
Is the engine wet sumping when sitting?
You say that you added a breather under the magneto. For this modification, as used on later alloy head engines to work, you also need to add a hole through the timing gallery into the crankcase which really needs the crankcases split to do. The breather hose from the spigot that should be screwed into the hole below the magneto should be connected to the back of the later style oil tank, the iron MSS oil tank does not have this connection. I made this modification to my Venom, including adding the connection to the tank, but also left the breather hole in the crankshaft. But, in my opinion, this modification is not necessary for an iron head engine.https://www.britbike.com/forums/ubbthreads.php/topics/229196/re-59-velocette-venom#Post229196https://www.britbike.com/forums/ubbthreads.php/topics/350698/re-59-velocette-venom#Post350698
My iron head MSS is quite sensitive to the oil level in the tank and even a slight overfill will result in excess oil in the PCC. Same for the gearbox oil level. I can easily monitor this as I run the PCC dry (relative term with Velos!) using an O-ring primary chain. The oil mist from the crank breather actually helps keep the engine shock absorber lubricated. I usually drain off a small amount of oil from the PCC every 500 miles or so.
The oil pumps seldom give trouble unless debris enters them. To remove the pump the engine needs to come apart as it is a shrink fit into the crankcase and heat is needed to move them. There is a "filter", actually it's a plug with reduced clearances that is designed to catch any large debris before entering the pump. This can easily be removed and checked. If you are getting good flow back the oil tank - it will be intermittent as the scavenge side of pump is of a higher flow capacity than the feed side - then I wouldn't go removing it at this stage.