I've no experience or knowledge about using SNP data in this format for estimating a phylogenetic tree.
My (strong!) preference when it comes to tree building is to use explicit probabilistic evolutionary-process based models - almost always focused, if working on nucleotide sequences, on the evolutionary process of base substitution.
There are lots and lots of software packages out there, that use such models, and which take as input a multiple sequence alignment of your sequences, rather than a list of SNPs.
Without, as I say, any experience working with a list such as you describe (maybe this is common practice in some contexts?!), I would rather recommend that you instead get your hands on data which can be transformed e.g. into a fasta format multiple sequence alignment file, which can be used (or adapted) for input to software such as PhyML, RAxML, MrBayes etc.
I notice, looking at the PLoS One progressiveMauve paper, that they say
"The alignment can also be used to extract variable sites for more traditional phylogenetic analyses. "
which suggest to me that you may be able to get something like this out of the aligner.