Is there a reliable free cell solver?
The solver you mention do solves this deal with 4 free cells.
For MS Freecell Deal #9371310
: TD 2S 8H 4S JC QC 6S 
: 2H 4C 7S 8S 9D KD 3D
: 5S 3C 9S 9H 7D AC KC
: 5D 7H 9C 5C AD 6D JD
: TC 4D 3H AS QD KS
: 3S 8C QS AH KH TS
: 2C QH 8D 4H JH JS
: 5H 2D 6C 6H TH 7C

Used the default settings, it solved it in few seconds: