Asada is tremendously talented. I'm not a fan but I would never deny her amazing abilities. She seems to be going through a bad patch at the moment, but hopefully she can come out the other side a stronger skater.
For my money, Kim is the best overall singles skater in the world at present but probably not the best overall jumper (though she's up there). And she does not, in fact, lip (in the traditional meaning of the word).
If I had to choose an overall best lady jumper I'd probably lean toward Nakano or maybe Ando. Nakano gets dinged for leg wrap (which I'm not crazy about) and hammered for micro-underrotation (which is just insane) but I think she's the overall best jumper among the ladies at present (part of which is defined in terms of consistency in landing jumps in competition).
Nakano is avoiding her nemesis triple loop for two years, and of course, her occasional 3-3s are never ratified even under the old system. Nakano's 3A's are downgraded four straight times. Ando has five different triples without edge errors. And she's the only lady to do the 3Lz+3Lo after Slutskaya. I'll concede she can challenge Asada when she masters a triple toeloop combo.