Reversing the level 180° is a test for repeatability; not true level.
Without working the calibration screws myself, it would be hard telling whether base, vial, or mount were at fault. The first method I use are matching feeler gauges, Jo blocks, reamer blanks [anything accurate] just at the ends. Then I pass a .001 smaller along the gap underneath.
This leads to a note about machine leveling. On a long bed to table, I start with a 2', 4' to 8' box beam level, dependent on space, another at 90°. Each are perched on matching 'supports' like 1-2-3's to bridge obstructions. This makes reading movement as it nears level, not 'twist'; very common in lathes. Then the good levels come out. Once I know the pitch of leveling screws [vertical movement per full turn] and distance between the supports, it simplifies estimates how far 3 of the corners need adjustment. I say 3 corners, not how many screws there are. Paint a stripe on the locknut, making incremental changes less of a guess.
One more helper; a pair of wedges; hardwood, aluminum, or bandsawn steel. The angle is shallow enough to fit between floor and machine base. Often trying to make final adjustments, too much compensation is made. OK. Before backing off, slip the wedge in; then back off the screw it will be carrying far less weight. Wedge can be tapped/ wiggled out as the screw just re-contacts the floor, it will be lower than before, just slightly.