your problem is in principle NP-hard. However, the hardest part of the problem is to determine whether a word is "unmoved" (these are the unmarked ones in my output, see also Re^3: diff of two strings). This can be done in O(nm) with this dynamic programming ansatz. How the words are finally printed out in printDiff based for example on uniqueness (insertion, but only in the second string) or moved position (in both strings, but a insertion/deletion) are IMHO trivial changes.
I do not understand your note and I still think the LCS is the way to go. Do you understand the algorithm? If yes, then please tell my why or when the LCS fails.
If you really want to use common substrings to construct a skeleton, try Tree::Suffix, which is also mentioned in my String::LCSS_XS module. But keep in mind that these modules are character based (so they are much slower without any re-encoding tricks) and that the free suffix tree/array implementations are in general not as good as they could be. Optimizing the lcs algorithm in C is really easy. See the wikipedia article for details. With the linear memory modification, the data should even fit in the cache for not too large strings.