You can get a more precise latitude (in the sense we use the term) measurement by measuring the angle of the ecliptic with the horizon. Shoot any two other bodies in the system that happen to be reasonably close to the horizon; with 8 to choose from, that shouldn't be hard (and assuming they're all pretty much coplanar, which I believe is the case). Your latitude is the angle between that line and a vertical line.
If the coplanarity constraint isn't met, you need an ephemeris to pull off the trick, but it still works.
Combine that with "solar latitude" as Leonard describes and you can get a very precise position fix. Actually, you'll get a couple of solutions, one on each side of the noon meridian, but (a) you'll usually have a rough idea where you are so you'll know which one to pick, and (b) failing that, you can disambiguate using a compass.