I'm not sure how easy it would be to implement, but I'd like the 4th on your list - a stat for 'Longest gap to previous log'. That could be interesting, and may encourage people to go find lonely caches.
To be honest, I don't understand your first two, and the third one I wouldn't be interested in because I'd have no influence over it at all. Plus archiving a cache after you found it would throw the stat to crap.