Brian,

I don't have the energy to write up a longer answer, but is this the following 
what you seek?

        P =: verb define
            4 P y
        :
            dc          =.  <: card =. x
            N           =.  y
            
            'm n'       =.  N #:~ 0 , dc
            |: (1 , n) + (1 , dc) * (,:&:i. -) m
        )
        
For a given  N  , that verb will produce all the pairs of  inc,width  which 
satisfy your cut-stipulations:

           P 38
         1 35
         2 32
         3 29
         4 26
         5 23
         6 20
         7 17
         8 14
         9 11
        10  8
        11  5
        12  2

            8  14 e. P  38
        1

           98 106 e. P 400
        1

The optional stipulation is satisfied with  {:@:P  .

-Dan
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