There are a few more I'm going back to remix to get a better sound based on what's been learned. 
 
Another trick is to load an MP3 of a song with keys/vocals, and use that as a reference. Listen to it (the one you like) then solo your keys, A/B and stare and compare, then mute your keys, and solo your vox A/B, stare and compare, and tweak. 
 
I'm going to be doing some of this with my older tunes later this Summer (God willing.) 

Piano chording or arps or both?
 
Spatial domain pretty well discussed here, cept depth of field...maybe a little verb on the keys to slide them back away from the front edge of the stage?
 
Frequency domain...you might could triple track (clone twice) the keys, EQ the three for a nice blend, lows, mids and highs, but pick the center band cutoffs so it directly competes with the voice, then work dynamics or automate levels so it subtly slides behind her vocals and then back out front during her rests. The listener's ear will try to compensate for the missing mids, and you don't want a whole lot of focus on a meandering hole in the middle of the piano, so you might play around with precise timing, and points of emphasis in the vocals.
 
When she hits one hard, it will come in over the top of the full spectrum piano anyway, and if she then backs off on the second or third note in that line, you could pull the meat out of the keys then, once she's in the middle of the uncompleted thought and already has the listeners attention.
 
You might even get a bit...evil...with it....
 
Let the piano ring out while she's building toward a peak, make them lean forward some, work to get her nuances, and once you have them reaching for her, pull back a little harder on the piano, use the extra room to bring her even further forward and smack 'em right in the chops with the peak of her vocal. If there's one word in there she really hammers, you can even pull back on her verb till the very end of the articulation, (and EQ as well) ,dry the middle of that word up completely, then sweep the verb back in on vocal just in time to leave a tail so it doesn't sound like she blipped into another room.
 
You know how certain upper mids can harsh your ears, right? Its a Darwin thing, so you can hear the toddler crying from underneath the overturned bookcase over the bassist and drummer finding the groove. You can blip in just a bit of that too, without the fatigue of a longer listening interval if the mood and arrangement will allow it.
 
Gotta stay with the feel of the song, yada yada, just some things you might try and see if they get you home.

jay tee 4303
 
Thanks for the additional, in-depth comments, much appreciated!
 
On this project (Casualty Of Love done ballad style), I ended up with the Tony Bennett approach after trying a number of styles, i.e. I panned the piano slightly left and with reverb as you suggest, slightly back and out of focus. I also took the suggestions above and used automation to bring the piano out during the interludes. I made a number of mixes (and I listened to countless renditions on YouTube) but came back to this as my preference over and over, by far.
 
Incidentally, the young singer travelled to St. Louis this past weekend and auditioned for The Voice with this same song but her mother tells me her nerves caused her to freeze up and she did not advance to L.A.. though she was asked to come back next year. But that is a whole 'nother issue to work on :)
 
Thanks again, some fine tips there to consider on her next project!

If you are liking the same mix day after day, you probably have it right!
 
Sounds like she's too young to run her thru the club circuit...but that would probably get her confidence up and disappear any nerve issues.
 
What's to fear from polite judges in a contest when you are used to dodging beer bottles and stray rounds?