Finish for aromatic cedar

I have two lovely pieces of cedar, which I am making into Go boards, a traditional Japanese game. I sealed the wood with a water-based matt varnish prior to applying lines using ink - my intention being to finish off with another coat of varnish to protect the lines.
My problem is that the cedar, which has been seasoned for about ten years, seems to be exuding some sort of sap which is reacting with the varnish in places, making it permanently sticky - particularly noticeable at the end grain, but also on the surface.
I will have to sand them back to bare wood now and start again. What I want to know is how to give a durable finish that will seal the wood sufficiently so that the ink lines will not bleed into the grain of the wood - without being made sticky by the aromatic sap/vapour. Ideally, I want a semi-matt finish.
Would Tung or Danish oil work? Another consideration is an oil based varnish mixed with turpentine. Some advice would be appreciated before I waste time and energy getting it wrong.
Many thanks, Donald.

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