Affordable quality mechanical watch movements such as ETA, Seiko, Miyota, and Orient can be rate adjusted to better than 5 seconds per day using a free program called Audacity. There is a learning curve to it. The how to YouTube videos are helpful. See links.
An excellent affordable mechanical watch suitable for underway celestial navigation is the Orient Ray II divers model which hacks and hand winds.
The Orient Flight model is another very accurate mechanical watch which would fit the navigation roll. This model doesn't hack or hand wind but is very easy to read in all light conditions.