BB shells are Predominantly open inside, to the tubes attached to it.
You would be be filling up the seat tube, chainstays,& ,down tube ends with the grease otherwise ..
My crank arms are far away from the bb so I would need a bunch of orings on either side
if you say so .. O ring + some rubber hose on each end , instead..
The act of putting the crank arm on is the force keeping the O ring against the Face of the cup
it wont tend to stay close enough on its own ...
Ive greased an wrapped pipe-cleaners around the spindle
before to try to get the BB grease to stay uncontaminated longer..
You could go out and look for another BB.. there were some made in past years
with a channel for the O ring in the cup's. edges.
the engineers want to move the Bearings further apart these days .
lighter stiffer faster ..