As usual, with a few of these comments....
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The idea of blending your tone and sending that one line to the PA is the best one. Unless you are touring with a soundguy and have worked with him on the blend in rehearsals, and when and it is and when it's not needed, it's a complete and total crapshoot that you'll get the blend you are looking for.
Work out that blend and send that to the PA. If you are using Kombat PA, the soundly (the good ones, anyway) that's mixing your band for the first and maybe only time will have enough to figure out.
When I was mixing, I liked to take bass bass lines, one DI (either a decent amp XLR out or a good DI that's AFTER all of your pedals and effects. Read that again.) as well as a mic on the cabinet. If this idea is appealing to you, you should put this on your technical rider and input list that you send out to the PA companies.