The Danish oil should work well for you Ray. Get yourself a baking pan or dish and pour the Danish oil in. Soak your basket in the oil using a chip brush to wet what isn’t soaking. After about five minutes, remove the item from the oil and wipe off the residual oil with a clean dust free rag or paper towel. Make sure you use some rubber gloves to do this. Wipe off all the oil and let it dry. Pour the oil back into the can. After the oil is dry, you can spray whatever topcoat you like.
Because of the cost of the Danish oil, I mix my own oil. I start with a quart size glass mason jar. If your wife does any canning, it should be easy to find a jar. I fill it half with the boiled linseed oil and half with mineral spirits. The oil brings out the color and grain of the wood, and the mineral spirits thins the oil so it easily soaks around your project and allow the oil to dry in about 24 hours.
I pour the oil back into the jar for the next use.