Depending on Kl-33N's cleaning level and your bag size you can go to a pay-to-dig site and grab as many fossils as you can and whatever is able to be dropped off for cleaning drop it off. this way you up his cleaning level by cleaning jewel rocks and new fossils even dark fossil rocks and you also get points for the ones he cleans that don't integrate.
Well, the EASIEST way is to just clean every fossil you acquire yourself since you'll get 10 DP for each perfect 100 fossil.
Of course, that's also extremely time consuming, tedious, and boring. So your next alternative is to collect as many fossils as you can and drop them off with KL33N. I think at the highest, he'll clean to a 90 success rate, so you won't be getting as many DP per fossil, but it's also less time consuming.
Basically you're just stuck grinding it out. --- (:3)--|--<