A gyroscopic roll stabilizer for a boat includes a flywheel shaft having a first end and an opposite second end. The flywheel shaft has first and second open-ended cavities formed on opposing ends. A first uneven seal encloses the first cavity, and a second uneven seal encloses the second cavity. The first and second uneven seals are both configured to provide asymmetric sealing such that greater resistance is provided against flow in a primary sealing direction, from a first side toward a second side, than in a secondary sealing direction, from the second side toward the first side. The first side of the second seal faces inward toward the second cavity, and the second side of the first seal faces inward toward the first cavity. The first and second seals are functionally inverted relative to each other. Related methods are also disclosed.