Dual Mono has the benefit of a heavy current draw or noise transmited up the PSU rails will not affect the other channel. A chip amp has good power supply rejection, so there will be less noise impact. If one channel draws the rail down, it could impact the power available to other channels.
How profound an effect? Most likely subtle with chip amps. Other designs may be profoundly impacted, though. You probably wouldn't notice a difference if you use a single psu for woofer and tweeter amps.
One word of caution - you describe your speakers as power hungry. If this means that their impedance dips to a low value, you might want to consider parallel LM3886s on fairly large heat sinks, at least for the woofers. You want to ensure that the protection circuit does not kick in, which it will if the chip gets too hot or tries to deliver more than its rated current. I had this proble with my LM4780 (two 3886s in one package) on a smallish sink, even at fairly low volumes. Going into protection does not sound nice.
You might also consider driving your woofers with a bridged/parallel quad of chips, which ought to give you around 200W peaks, and be a bit more likely to stay out of protection. Although more expensive than a single chip, it is still probably cheaper suitable than discrete amps.
Take a look at AKSA's offerings, the Leach amp or Rod Elliot's P-101 or P-3A for discrete amp options. I haven't heard AKSA or Elliot amps, but have a strong preference for the Leach over my chip amps, although they were not nearly as refined as the ones you are considering.