Kalium's suggestion would in fact satisfy me -- it captures the distinction between someone who went to college/graduate school but didn't finish and someone who never went in the first place.

I disagree with your comment above that

the distinction between "started work on degree X, but abandoned it" and "currently working towards degree X" is almost as large as that between either of those and "never attempted degree X.

For a completely hypothetical example, let

A = someone with a B.A. who spent 6 years in a Ph.D. program and left without finishing

B = someone with a B.A. currently in a Ph.D. program who hasn't finished yet

C = someone who completed a Ph.D

and

D = someone with a B.A. who never entered a Ph.D. program..

My view is that there should be some notion of "education level" that clusters together A,B, and C, as distinct from D; but "highest degree attained" clusters A,B, and D as distinct from C, and your proposal seems to put A, D in one cluster and B, C in another.