Roughly 1/16" of axial play on the cone pulley and bull gear doesn't seem excessive to me (but there are others here far more knowledgeable than myself). The cone pulley has to be able to spin freely when it isn't locked to the bull gear, of course, in order to use your back gears. If the oil appears to be coming from between the cone pulley and the bull gear, then someone likely over-oiled. The oil port (screw) just lets you apply oil directly to the spindle shaft – it can definitely seep axially along the spindle.
I'd just wipe up the excess and not worry about it as long as you are talking about axial play (along the spindle axis) and not radial play (too loose a fit on the spindle).
I'm unclear what bushings you replaced, though. Are you talking about the oilite bearings between the cone pulley assembly and the spindle in the headstock, or the bushings on the drive assembly shaft? That is, did you replace something inside the headstock casting, or something on the rotating shaft that the motor belt attaches to?
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Rex