As tagged correctly, this is a multiple sequence alignment problem, so pairwise/database alignment tools (BLAST or maybe B/LASTZ as mentioned above) are not an option.
So well understood tools such as ClustalW, or T-Coffe, or DIALIGN, might already do the job. Try low gap extension/opening costs. I would try a well-known algorithm and try the more 'esoteric' stuff later on, and only if that doesn't give good results.
Better than ClustalW maybe in your case
Dialign: It uses no gap-costs.
This approach can be used for both global and local alignment, but it is particularly successful in situations where sequences share only local homologies. (From the BiBiServ description)
This seems to fit your case quite well.
Another possibility would be to mask out the portions of each sequence that is a priori known to be less conserved. That requires to have knowledge about each sequence and to manually design a mask. Or even a vector of base-specific weights, but I don't know any MSA tool that takes such input. If you find one, please post it here :)
Small update: another aligner can use an arbitrary (but less than 250) alphabet: http://www.vmatch.de/