Maybe you should gift caravans with good things with lots of mugs(or food, or everything you use as wealth maker) and burn/drown caravans with wood? "Giantanimals the live giant-cages of animals" and "Moonshine the shiny moon-loads of booze" corporations will get richer and you will take care of their rivals, "Woodweapons the carping wood-wagons of weapons", "Catscats the breeding meow-cats of domination" and "Deadanimals the dead awesome-animals of miasma". And, of course, they will satisfy your "special" interests, because they know that in another case you will rename them to "Burntelves the funny warm-piles of ashes".
Or, simplier, elven race will be screened with patented Eugenic Magma Pullthelever/Eugenic Goblindrived Slowdrowner and clever elves will some day be the only elves in civ you're trading with. Remember, there's never too many tree-huggers.
Or you could kill their liason and get a bunch of free +elf cages+ and *unicorn cages* every year. Elves are good to be suddenly freed from their cages when the vile forces of darkness(elf-loving nobles, in example) arrive, unicorns are untamable but their children are.
But at first make a huge wood stockpile, not necessarily accessable. AFAIK, the bigger stockpiles will force them to bring less wood.