Highly heterozygous reads mapping
I believe you may be able to map your reads, but I don't know how to do that with minimap2. 

I recommend running gsnap, which is more SNP tolerant and provides a number of parameters which are likely to help.

For instance, I believe that most aligners will treat 'N' characters as mismatches when you align. GSNAP has parameters to account for this. 

--query-unk-mismatch=INT       Whether to count unknown (N) characters in the query as a mismatch
                               (0=no (default), 1=yes)
--genome-unk-mismatch=INT      Whether to count unknown (N) characters in the genome as a mismatch
                               (0=no, 1=yes (default))


It also has a mismatch parameter similar to the one you described for minimap2.

-m, --max-mismatches=FLOAT     Maximum number of mismatches allowed


Try running with the 'genome-unk-mismatch' parameter above (with the masked reference). That may be your best bet. There are also other parameters that may help, but this should be a good start.