Your comment on patterns in column 4 led me to notice that there's a pattern in the optimal dissections in that column that can easily be extended. Here's a new dissector that implements this and hence fills in 27,4 and 29,4:

def col4_dissector(n,m):
    if m != 4: return []
    if n % 2 == 0: return []
    d = (n-1)/2
    bit = Fraction(1, d)
    return [([[(2, (n*bit,) * d), (2, ((n-2)*bit,) * d + (2,))],
              [(1, (2, 2)), (n - 1, (n*bit, (n-2)*bit))]],
             "general pattern for m = 4, n odd")]

Sorry to provide you with additional results just when you thought you'd finished.