The Stage only has a few drum loops, and an arpeggiator, not styles per se. That is the GW-8 with a 61 keyboard. Nothing to stop you recording your arranger's audio output to MP3 for each song, though, and using the built-in player for backing, or using a drums SMF of the tune's groove you want to do, and do the LH bass thing like he does in the demo (or a bass and drums SMF of the song if you prefer). Plenty of options, but no styles, per se...

The problem you are having with the piano is because you use a mono amp, and the phasing on the Yamaha's main piano is particularly bad (although all stereo piano sounds suffer to one degree or another when collapsed to mono). If you change to a stereo PA, this should go away, IMO...

My G70's piano changes a BIT when played in mono, but not as much as Yamaha's (I'd love to hear how well the new T3 piano collapses to mono... anyone?). It's just the nature of playing true stereo material through a mono amp...

I have a nasty feeling Yamaha exaggerate the width by adjusting the phase of the L & R sides a bit (it's how cheaper effects are made to sound wider than they really are) to make it sound impressive on the built in speakers, but when collapsed to mono it introduces more phasing and the resultant EQ weirdness than leaving the thing alone and having a less dramatic stereo speaker sound. But this is just conjecture on my part...

I must admit, most of what I'd like to see in a simple stage keyboard (rather than an arranger) seems to have been nailed with the Juno Stage. As long as the MIDI is flexible enough to add maybe a Nord for Hammond stuff, this might be almost perfect...