Since the 4x is "silent" ... build a custom rack that puts the 970 really close to the back of the Korg, so you can plug the outputs of the Korg into the Yamaha. Your living room will look neater, no sound system needed for home use. (Maybe get a teeny bass amp, or sub if it makes you happier)
Now, you get the advantage of the better key feel of the Korg, triggering the combined goodness of both architectures, with stellar vocal effects, and oodles of sonic choices. Save your money - make two become one (Sounds like the Spice Girls?)
That's what I'd do.