Dark rum without whiskey taste

Try a bottle of Denizen Merchant Reserve. You can also try a Barnacle 8 or 12 year but they can be a little on the sweet side. 

Most aged spirits use ex bourbon barrels because they're that much cheaper and accessable. I would look out for sherry, madiera or cognac cask rums. Alternatively go for the sweeter rums with added sugar - they tend not to carry so much of the bourbon cask influence.

Try dos maderas 5+5.