Doesn't look like it will work when sorted descending either. Next strategy will be to construct a directed graph of the fits relationships and somehow figure out the tree with the largest height.

i 0, origPosn 7, start 0, currentLen 1, START   6       5       4       3       2       1
i 1, origPosn 4, start 0, currentLen 1, FITS    14      13      12      11      10      9
i 2, origPosn 2, start 0, currentLen 2, START   23      15      11      9       7       3
i 3, origPosn 1, start 2, currentLen 1, START   30      20      10      5       2       1
i 4, origPosn 5, start 3, currentLen 1, FITS    31      27      18      17      8       4
i 5, origPosn 6, start 3, currentLen 2, FITS    44      44      41      32      19      13
i 6, origPosn 3, start 3, currentLen 3, START   50      40      34      24      14      4
i 7, origPosn 8, start 6, currentLen 1, START   80      47      37      21      18      9