How about using a hash, with the key being the string item, and the value being an index, which gets incremented each time you find a new string.

Then you can sort numerically on the values of the hash to get the original order.

Is that what you're looking for?

Update:  After rereading your question more carefully, it looks like that doesn't work.  But perhaps if you use a hash where the value corresponding to each string is a hash, within which each key is the number of times "Start" has been found, and the value is the index within that sublist.  You'll know an item isn't in a given sublist, because the corresponding key won't be defined.

For example:

Start      # This is sublist #1
Alpha      #     $p->{'Alpha'}->{'1'} => 1
Beta       #     $p->{'Beta'}->{'1'} => 2
Start      # This is sublist #2
Epsilon    #     $p->{'Epsilon'}->{'2'} => 1
Zeta       #     $p->{'Zeta'}->{'2'} => 2
Start      # This is sublist #3
Beta       #     $p->{'Beta'}->{'3'} => 1
Gamma      #     $p->{'Gamma'}->{'3'} => 2
Zeta       #     $p->{'Zeta'}->{'3'} => 3
Start      # This is sublist #4
Alpha      #     $p->{'Alpha'}->{'4'} => 1
Gamma      #     $p->{'Gamma'}->{'4'} => 2
Delta      #     $p->{'Delta'}->{'4'} => 3
Epsilon    #     $p->{'Epsilon'}->{'4'} => 4

would give a hash like:

    $p = {
        'Alpha' => {
            # Note 'Alpha' doesn't appear in sublist #2 or #3
            1 => 1,  # Alpha is #1 in the 1st sublist
            4 => 1,  # Alpha is #1 in the 4th sublist
        },
        'Beta' => {
            1 => 2,
            3 => 1,
        },
        'Epsilon' => {
            2 => 1,
            4 => 4,
        },
        'Zeta' => {
            2 => 2,
            3 => 3,
        },
        'Gamma' => {
            3 => 2,
            4 => 2,
        },
        'Delta' => {
            4 => 3,
        },
    };
[download]

Does something like that help you?