I actually had a similar discussion w/ Effie@Savage today.
I was looking to get a LH Hog Hunter made, and as we were going over the features I wanted somehow "iron sights" became "detachable box magazine"; she directed me to the precision carbine.
With me pointing out it's lack of sights and (ahem) slightly higher price, she asked if the DBM was important. I said no, so back to the Hog Hunter style we went.
Good news is it's possible to get a LH one made up, and at not too horrible a premium... just not w/ a green stock but black/grey is fine with me.
Luck on your project.