I do mine a bit differently. I take a piece of pine or apple or maple cut in a circle for the bottom, about 1/2 inch thick and about a 1/4 inch diameter LARGER than the diameter of the bottom tube that the mug. Push it into place in the bottom of the tube and boil the whole thing in vegetable oil. As it cools the leather shrinks around the wood in the bottom. Once the mug is cool I dip it in melted paraffin wax for just a second. When I pull and dump it I swirl the left over paraffin in the bottom of the mug and set it upside down to dry. If the coat on the outside is too thick for your liking the put it in the over on warm (about 125-150 degrees) for 2-5 min. This doesn't make dishwasher or hot fluid safe mugs but they stand up to any type of alcohol (I've tested them extensively). This is the type that you commonly see at the Ren Faires.
Hope this helps out.
~Kevin~