I had horriffic emulsion problems on my late 350 bullet (2007) which had the oil tank breather. Catch can regularly full.
Even after replacing it with a straight duckbill, it still clogged and needed clearing every 300 miles or so (blowing through into a paper towel every other fuel stop), even after averaging 150miles of daily use for 3 months. The emulsion problem disappeared entirely when I fitted one of our hosts scavenge bypass valves. I have no idea why.
I still felt it wasn't breathing properly so went the whole hog and drilled a hole in the crankcase! Drilled and tapped it and fitted a nipple.
I also did a bit of a quick and dirty experiment to measure the volume of gas it breathed out with the various confugurations (including with and without the oil tank vented). Basically by seeing how quickly it would displace 750ml of gas (a wine bottle).
There was little to no difference in how well it breathes via the oil tank and via the crankcase however if the oil tank was left open to atmosphere with the breather on the crankcase, it pushed out around 10X as much gas! suggesting it was sucking air in through the oil tank and blowing it out through the crankcase breather. I videoed it.
https://youtu.be/ET0Rv4fh-Yc
My own thought is that venting through the oil tank is inherantly unhelpful and effectively a bodge to make late models pass emissions tests. The "modification" is essentially a 4mm hole drilled between the crankcase and oil tank. It looks like it's been done with a pistol drill at the factory .
I have blocked this hole off on both my bikes by tapping and inserting a tapered-threaded bolt from the oil tank side and re-instated a crankcase breather (using the above hole on my 350 and by having the blank breather stub drilled out on my 2004 612).
My 350 has a stub on the timing chest (originally for the "return" from the catch-can) which I am going to try both blanked and open. I suspect it will act as a breather for the rocker area with which it has a direct connection. If this works, I'll fit a similar breather stub in the blanking plate I fitted to the 612 to cover the hole left by removing the distributor.