The cake took a long time to finish and looked to be slightly oily
Did the recipe call for fully melted butter and you used partially melted butter?
Thank you. No. Soft butter.
I fear that melted butter does not react in the same way with flour and so the cake may be greasy as a consequence
Oh I see....a creaming method cake relies on the butter being in a solid state to perform the way its supposed to. Now, sometimes a cake recipe can be adapted to use melted butter but the method would change and the result will change. You won't have the volume and structure with melted butter as you would with creamed butter. You may prefer one over the other, but honestly its difficult to say unless you taste it. I wouldn't say its ruined....some of my quick bread recipes use melted butter and they may come across as moist in a slightly greasy way, but it just may not be what you had expected.
Donald ...cut into it (somewhere inconspicuous if needed) and taste.
Would you want to eat it?
If Yes, douse with appropriate liquor and age until Christmas.
If not a good taste or texture, make another one for Christmas.
(You may be abke to salvage the 1st one as sweet toast, parfait with ice cream or whipped cream, etc).