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.