I dont think barrels are available from T/C anymore (call to check), but you will find used ones on here and other places.  Sometimes a new old stock one shows up.  Im not sure if Green Mountain Barrels makes a drop in barrel for the New Englander.  it would be on their website and they are excellent quality.  T/C made 12 gauge barrels and rifle barrels for the gun.  It seems barrels for your gun are just a hair cheaper than for a Hawken but I dont know why.
Ive never had a left hand gun but I would think the hammer would be on the other side of the frame, along with the nipple.