After some pondering, I have an answer to my own question (to which I welcome feedback). I think the most straight-forward way to handle this is to create a new factor that is a cross-combination of the two factors of interest. And so, the data would look like this:
ID Factor A Factor B Score Cross-Factor
1 a alpha 0.1 a-alpha
2 a alpha 0.2 a-alpha
3 b beta 0.3 b-beta
4 b gamma 0.4 b-gamma
5 b delta 0.5 b-delta
6 c beta 0.6 c-beta
7 c gamma 0.7 c-gamma
8 c delta 0.8 c-delta
The model would then include a single factor with 7 levels. I can interpret the factor relative to the a-alpha level using contrasts to extract the change from baseline to whatever combination of the cross-factor I'm interested in, or between means of other level comparisons. In fact, I could set up the following contrast matrix using [the method outlined on the UCLA page][1], as one example of a contrast matrix.
*Original Matrix*
[,1] [,2] [,3] [,4] [,5] [,6] [,7]
[1,] 1 3 3 1 0 0 0
[2,] 0 -1 0 0 0 0 1
[3,] 0 -1 0 0 1 0 -1
[4,] 0 -1 0 0 -1 0 0
[5,] 0 0 -1 0 0 0 1
[6,] 0 0 -1 0 0 1 -1
[7,] 0 0 -1 1 0 -1 0
If this matrix is transposed, solved, and the first column removed to create a contrast matrix, the resulting coefficients would be the following comparisons:
1. Intercept is the baseline mean value (*a-alpha*)
2. Coefficient 1: Difference between baseline and average of all severity levels of *b*
3. Coefficient 2: Difference between baseline and average of all severity levels of *c*
4. Coefficient 3: Difference between baseline and the most severe form of *c* (*c-delta*)
5. Coefficient 4: Difference between the moderate and most severe forms of *b*
6. Coefficient 5: Difference between the moderate and most severe forms of *c*
7. Coefficient 6: Difference between mean of both mild forms and the mean of the moderate forms.
[1]: http://www.ats.ucla.edu/stat/r/library/contrast_coding.htm#User