Can one rely on the ladle as a keli sheini in order to (on Shabbat) put cheese on top of pareve chili once that pareve chili has been ladled from the crock pot insert (removed from the heating element) into a bowl?
If I understand you correctly, the question is whether the bowl is a keli shelishi, since we would be machmir for Kalei HaBishul if it were only a keli sheini. I think definitely yes.
First, it is not clear that we have to be choshesh that everything might be a Kalei HaBishul (see Shulchan Arukh OC 318:5 and Mishnah Berurah 318:42).
Second, cheese is made from pasteurized milk, so there is a reasonable argument that it is already מבושל and by solids אין בישול אחר בישול (there is a debate in the poskim whether pasteurized milk is considered מבושל כל צרכו. Rav Moshe (Iggrot Moshe OC 4:74, Bishul 6) and Rav Shlomo Zalman Auerbach (Shemirat Shabbat KeHilkhatah 1:61 and footnote there) rule that it is.
And finally, since you are removing it from the insert off the fire, and the ladle is never heated directly by the fire, there is extremely strong reason to assume that it is a keli sheini.