I don't know anything about cygwin (except that many people have trouble getting stuff working on it), but I do know that if you could get access to a Linux machine (server, virtual box, dual boot, standard installation) things would get far easier for you.

Re samtools, just compile the source code. I haven't used GATK on cygwin

Even though you set running environment well, you really want to use samtools or GATK to call big bam data on your Windows?