How are you so sure it starved of oil? For me to say this, I would have to have the oil pan for a BX in my hand and see where the pick up is. I'm not saying it isn't possible, I just haven't seen it on my BX. I have also gone up and down hills, that if they were any steeper, they we be very unsafe.
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I have worked on them enough to tell you that the lower sump is the redundant oil reservoir and if the oil flows out of it no oil returning, the engine is wadded.
The twin slopes in the mine where I used to work are 21 degrees and they engines on our boss buggies had to be overfilled- filled high mark upper sump and filled lower sump to provide proper lubrication and for oil to reach the pump and strainer hence 2 dipsticks in all the small engines as you can have a filled lower sump and a short on oil upper sump and still kill it.
Dont forget you are sitting two feet or so above the ground which makes your eyes and brain think its even steeper due to your line of sight vision and you would have wadded your engine if it was steeper.
Rack railways are not as steep as funiculars but are still very steep and the engines are tilted down creating a level engine while ascending to counter the angle of attack required to ascend the funicular rail path and incline.
funicular rail lines are much steeper in many places and are unable to use diesels for propulsion and have to have a counterbalanced system with a second tram to provide energy to move in opposite directions on the funicular.
Terraced rice paddies are very steep and often located above 21 degrees in incline on the mountains and hillsides-hence the 2 sumps to provide oil pressure when riding down the decline, the lower sump and oil intake is always flooded when when ascending the incline.
the rice paddy terrace farms are why the smaller engines has two sumps as the wadded a lot of the small diesels before they found out what killed them all.
It wont hurt the crancase any as the breather relieves all the crankcase pressure anyway.
A tractors center of gravity is quite a bit higher and above the oil sump or crank so that an entirely different animal versus oil pumping
Thats why the tilt meters are so nice to have in the tractor to remind you about the center of gravity and how little wiggle room you have.
Perhaps it may be simpler to just blow the snow over the bank
and not worry about pushing it from now on?
Granted I have no knowledge of your snow removal needs but that seems to be the lesser of two evils.