"Did America export wood to England?"...
Beginning in colonial times, literally millions of board feet every year. The rough figure for 1792 is approximately 1,300 tons. I have this fugure broken down into board feet and by type in my notes somewhere but most of this was hardwoods for the simple reason that soft woods were readily available to the British timber market from Russia and the Baltic - a much shorter distance and generally lower prices than American wood.
Exports included maple gunstocks... something I have documentary proof of for 1817... the Ketland brothers bought two or three huge tracts of timbered land in Pennsylvania for the black walnut.
As to English vs. American walnut... all walnuts grown in America as a fruit tree were "English". The fruit of the American walnut tree is virtually inedible. As late as the beginning of the 20th century the distinction was made between them by referring to the American nuts as "pig nuts" (i.e. good only to feed to pigs) and "English Walnuts" which were the ones you ate. My grandmother (b.1893) still used these terms.
Also, walnut is not indegenous to England. It only arrived in the middle to late 16th century, originally from Persia via eastern Europe. This is why walnut stocks on 17th century English guns are virtually unknown - there were no trees large enough yet to make a stock from. Most 17th century stocks are Beech. Walnut trees that were big enough to make a gun stock from were much more valuable for their nuts. American colonists started planting the "English" tree as soon as they arrived. While you can tell the difference between the woods, you can't tell where it was grown so its perfectly possible that "English" walnut was even exported to England.
With a few reservations, the whole business of saying where a gun came from by the type of wood in the stock is a myth. Timber was the largest single export of the American colonies and the early Republic and Britain was our biggest customer.
