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I know BLO is often used, but you might consider one of the tung oil based wipe on products. I kinda like Daly's Ben Matte--there be others. Dries/cures faster so yer 'skins don't stick on the warm 'voo you are going to attend Labor Day...I have some rondy stuff I finished with 100% tung about 30 years ago, and they still look good.
Bison Horn, That is a very nice looking chair. You should offer them for sale since you know how to build them.