The valves have already been check for the gap and I even did a check to feel for pressure escaping like the older Briggs. I had that one where the intake valve had worn into the seat and lost all clearance and it was raw fuel doing the venturi effect the opposite way out at the air filter. The new used Briggs is in spec, I measured with a feeler gauge.
There is oil that is not thinned out with any gasoline in it that I found dripping just a few drops under the bike. I saw the protective cover that I put over the engine and carb on that side of the bike, inside near the bottom air opening in the air filter covered with a sheen of oil.
You mention to use Scotch Brite to try to keep the oil from, I think you say going past that sort of reed valve in the breather. I have seen stuff like that in some of the breathers of older parts for Briggs that I owned in the past. The breathers that I have now are crimp metal sealed shut. It would be difficult to open and reseal the breather to add this. I also would wonder if there should already be the stuff in there. Or also if not would it interfere with that reed valve operation if stuffing it with any or more of Scotch Brite.
Just to be sure I would not think Scotch Brite is OK to add inside the area with the valves, springs, and tappets.
The oil mist or maybe droplets as since I have the engine unfortunately tilted back (not forward) maybe 15 degrees, has probably too much oil getting through the hole from the crankcase by the cam shaft up into the valve springs area. I have a hose that run in a downward sideways direction to the air filter case opening for the oil mist to be burnt along with the carb intake air. Maybe the engine angle again makes it so the oil cannot go back in to the engine when you turn it off.
That breather, I am not sure how oil can go back into the engine anyway, if the breather reed valve seals perfect, if I did have gravity working for me if the air filter was higher than the breather. It is not and I am not planning on changing this design, but I learned that the forward lean of an engine to max 15 degrees could have been a better choice. Others on MB show not problem with breather having so much mist getting into the filter.
Lucky I am using no longer a paper air filter as I made my own foam filter to use with that special oil. I don't need oil for the filter now, laugh! Paper air filter cloggs when wet with fuel, not sure about oil spray.
An oil separator is something that is an idea. I would empty it once an a while and keep a check on the oil fill level in the engine too. I tought maybe a 12 oz steel can to use. I would have a hose run through the top down the middle to an inch of the can bottom. There would be foam half way up to the top of the can. A hold in the side of the can by the top would be the output. That output would have less oil spray and hopefully just the vapors that would be routed to burn along with the air filter intake.
I am wondering if I do nothing, then aside from the few drips of oil, I was concerned that the oil may clogged the foam air filter and choke the engine to a stop. This is quite similar to having fuel doing clogging. At least I can say fuel is not a problem now.
There are two clutches and the pawl clutch to the recoil starter, I understand about the fiber washer can be missing and still work.
You mention the squealing sound and putting some oil in there where there is that felt for the shaft that the pawl clutch rides on. Thanks I forgot to do that on this engine as I remember a tech at the shop mentioned this too. To note, he also said that the ball bearings should not have any oil and remain dry to operate. I understand where you also mention about a high temp grease that would not migrate and used sparingly.
The other clutch I use for the power train, I oiled the brass bushing and under engine power it runs and is just a little nosier than the belt clutch I had been using. Both would make quite a bit of noise when rolling the bike with engine off. The bell has to spin 13 or as before 20 times for one revolution of the rear wheel. That is when it is noisy. I would actually remove the belt connection to the rear wheel for any long distance I would want to push the bike. And for storage, the belt would be best to take tension off it anyway.