That doesn't actually work. You can't measure local noon accurately enough for it to give a useful longitude. My celestial navigation textbook estimates the acc

That doesn't actually work. You can't measure local noon accurately enough for it to give a useful longitude. My celestial navigation textbook estimates the accuracy of this method as 15' under the best possible circumstances, and 40' under more realistic circumstances. Even if you ignore this issue and assume you could somehow measure local noon exactly, you still would need almanac data in order to do the correction. Once you are involving almanac data, it stops mattering if local noon has any connection at all to 12:00 on your clock.