The real trick is to give yourself the option when you want it...
Try setting up the LH sound so that very light playing makes it not sound, only harder hits (say 40vel or what feels good) makes it sound. The arranger will still get the chord recognition whether it sounds or not. Now you can use sounds like horns or saxes, Rhodes, stuff like that that you may not want ringing out on the one every chord change, but can be put in to emphasize beats, stuff like that.
Another trick to open up what you can do with the LH is to combine that (or have the sound right down to the lowest strengths) with PianoStyle chord recognition. Now, unless you play THREE notes, the chord won't change. So you can play the chord at the 'one' (I still like to set it up so light touch doesn't sound, though), but single and dual notes don't change the chord recognition. Do this with a string sound, or say muted t'bones, French horns, synths, whatever, and you can chord AND play counter lines, or play simple chords then add the extensions just to your playing, not the accompaniment (cool to do 6/9's, maj7/9's etc. while the accompaniment stays on basic maj/min or open 5th chord patterns).
Another way to use this is to have say a bass 'pop' or slap, that ONLY sounds at the highest velocities. You can now chord, then add in a few bass tricks to give the bassline a bit of variety.
Yet another option, if you have a swell pedal, is set it up so it ONLY swells the LH sound. Now you have full control of when the LH sound is heard and when it is not.
I'm sure you can all think of many ways to use tricks like these... Seems a shame to use half of your hands to do little more than trigger the arranger's accompaniment! Doubling what YOU play allows you to switch off some of the arranger's Parts, and get something a bit less repetitive.
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An arranger is just a tool. What matters is what you build with it..!