Thank you for your interest in our paper. With more recent versions of fasttree, modification of the code should no longer be necessary. Instead, you can compile it with a flag indicating double precision:

http://www.microbesonline.org/fasttree/#BranchLen

Regarding the outgroup, you could use a strain from the early 1990ies like this one:

https://www.fludb.org/brc/fluStrainDetails.spg?strainName=A/Beijing/32/1992(H3N2)&decorator=influenza