Thank you for your reply! That seems to solve much of the issue, but there are still many unexplained observations. My 'underemployed' variable subtracts EDTAINMENT (which I just take the top five values of SCHL and put them on that scale) from the BLS typical required education by occupation.
Example: Required professional or doctoral degree = 5. Educational attainment less than high school = 0. 'underemployed' = 0 - 5 = -5 in that scenario.
Some stats for reference:
mean of 'FOCCP' when 'underemployed' < -4
0.8864541832669323 i.e. 88.64% of observations
mean of 'FOCCP' when 'underemployed' >= -4
0.15477719436066595 i.e. 15.48% of observations
mean of 'FSCHLP' when 'underemployed' < -4
0.6633466135458167 i.e. 66.33% of observations
mean of 'FSCHLP' when 'underemployed' >= -4
0.07940061918797757 i.e. 7.94% of observations
Now I feel somewhat alarmed by how much imputation there is...