Remember MAST's basic task is to score sequences for their
combined match to
all of the motifs in your input motif file. MAST identifies the best match to each motif in a given sequence, and then multiplies the p-values of those best matches to get an overall score for the sequence. The idea is to identify those sequences that contain a good match to
all the motifs in your file. This is typically used to identify promoter sequences that binding sites to known co-regulating transcript factors. If you have motifs A, B, and C MAST is only going to report those sequences that have good matches to A and B and C. If you have a sequences with a perfect match to A, but no matches to B and C, then MAST is not going to report that match to A.
If your motifs are highly similar to each other (highly correlated) this becomes a problem for MAST. If you have motifs A, and B, that are very similar to each other, then the best match to A in a given sequence might also be the best match to B in that sequence, but they aren't distinct sites. That's why MAST's default behavior is to not consider motifs that are almost identical to motifs that have already been considered. You can turn this off by unchecking the checkbox "Remove redundant motifs from query?"., but given that your motifs are nearly identical, the MAST results wouldn't be reliable.
I'm not clear what your overall goal is, but this makes me think that MAST is not the appropriate tool for you, and you probably should be using FIMO. It really sounds like you want to find individual matches to your motifs.