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.