I have been doing some ancient DNA bioinformatics for a while now and have been using the bwa aln command.
When using this command with ancient DNA it is recommended to disable seeding. This slows down alignments somewhat but allows the damaged DNA sequences to be aligned, the characteristic damage is a C->T transition at the 3' end of the sequenced fragments. For instance I use the parameters -l 1024 (to disable seeding) -o 2 (increase gap open slightly) and -n 0.03 (reduce the edit distance slightly). These parameters were taken from this paper
Your problem seems to be very similar in nature in that it introduces mismatches that are similar to sequencing errors. From what I understood from the paper bwa mem was designed to be robust to this type of errors.
Hi, you may want to try the GPU program MaxSSmap that is designed for aligning divergent reads to genomes. We used it to map ancient DNA reads and compared to BWA MEM it produced many more high quality alignments. You may also want to look into NextGenMap which also achieved a higher mapping rate BWA MEM.