Hey, I haven’t used tung oil, but I have used Tru-oil. It’s described as a gunstock oil, but it’s used by many guitar builders. It can be applied and buffed to a lacquer like finish, or easily made to look satin. I apply thinned 50/50 with thinners, and apply many thin coats. You have to be patient and allow 24 hours between coats, and rub with 0000 wire wool too before each coat. If you need a satin look, you just need to use 0000 after your final coat has cured. I usually let that last coat cure for 3 or 4 days before buffing with the wool.
Staining burl wood doesn’t always achieve what’s in your head. I find it absorbs stain at different rates and can be blotchy. I have done it using Kedo powder stains (water based), but I now tend to seal the wood, apply a few clear coats, and then apply tinted lacquer to get where I need to be. Then clear coats to finish off.