Ideas for my linoleum topped table

I have a great linoleum topped kitchen table from my great aunt....she had it since 1935 when they first built their home....the trouble is it had leaves that drop and slide back under the full the leaves are now a different colour from the top! The rest of the table and four chairs are oak that I will redo (I.e. strip restain and reglue) but that linoleum defeats me. Any ideas? Don't want to strip it, but perhaps repaint? And how? Thanks for any help (it can't be taken off too solid and corners and sides wrap around with non straight edges) (great work in the old days)

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