In all fairness, you are hearing something tweaked for stereo through a mono system when you play through the Compact.

Other than the true stereo pianos (don't really know about the PA800, but the Yamaha's have terrible phase issues going to mono), you aren't really having THAT much phase issues, but you WILL get volume and mix perception differences.

If you tweak your setups to sound their best through a mono rig, a lot of the bad you hear will mostly go away, at least as far as losing pads and effects. Yes, you lose the stereo, but you'll actually be able to HEAR the pad, EQ up the bells, etc.

No, IMO it won't ever sound as good through the mono system, but you CAN make it sound better than simply using your stereo performances untouched on a mono rig.