I thought this was a Medic hat, not a Soldier one. The high end might be a bit high but unless someone prices something from one of those unpriced hat sales I can't rule out anything as an outlier, whether low or high.

Useful Sales:

Sold for 55 keys = ~2.9

http://www.tf2outpost.com/trade/18900339

Sold for Disco Beat Down Hot Dogger (~2.5) + Orbiting Fire Familar Fez (~1.1) = ~3.6

http://www.tf2outpost.com/trade/18884807 (Dog and Fez)

http://www.tf2outpost.com/trade/18885822 (Valley)

Less Useful Sales with unpriced hats:

Offered on (and sold for) a Hellfire Glengarry Bonnet (???) alongside a Green Energy Prancer's Pride (~1.9)

http://www.tf2outpost.com/trade/17211466

Sold alongside a Terror Watt Hotties Hoodie (???) for a Cloud 9 Towering Pillar (~3.9)

http://www.tf2outpost.com/trade/18903983

Sold for a Green Black Hole Sultan's Ceremonial (???)

http://www.tf2outpost.com/trade/18885822