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Bulleit Rye is pretty decent for mass produced stuff, but I think you'll have to experiment. Living in the SW you'll pay a premium for bourbon as it's region specific (Kentucky), but it seems like new distilleries are opening all over the US now and probably producing some interesting stuff like blue corn whiskey (native to NM, btw). Think global, drink local, or something like that.
I think if you're trying to ultimately replace malt with bourbon, you're in for disappointment. You might find some of the rye whiskey interesting though. And Jameson tends to be available at a reasonable price.