Upgrading front 3 speakers to GoldenEar Triton Reference or B&W Nautilus 800?

You wouldn't need another amp to bi-wire the B&Ws.  Just get internally bi-wired cables that have one connection on the amp side and two on the speaker end, or attach two cables to the same output on the amp if you're running a full shotgun pair. 

And yes, I absolutely do think that highly of B&W center speakers.  I have a feeling it'll sound much better than a ribbon tweeter sandwiched between midrange drivers as with your XXL center. 

Soix

I have never bi-wired before, but  if I do as you suggest, that seems to me that I will be using only 1 channel of the Classé (which is 5 x 300w) and send basically only 300 watts to each speaker, which, from what I have read, may not be enough power for those Natilus 800 speakers. If I actually use 300w for the top and another 300w for the bottom of each speaker, it may give the speaker that little extra to be a little smoother sound.
What are your thoughts on this scenario?

Steve

ONLY 300 Watts???  That's a ton of power that should drive almost any speaker available.  Just as an example, back in 2009 Kal Rubinson ran the 802Ds with the lower powered CA-5200 just fine (https://www.stereophile.com/musicintheround/music_in_the_round_36/index.html), so I'd be shocked if your 5300 didn't have plenty of juice to fully drive 800s without biamping.  The 800s are 90dB efficient but do drop below 4 Ohms through a good part of the midrange, which does make them more difficult to drive.  But here's a quote from the Classe website regarding your amp:

"* Specifications for output into 4 ohms are omitted because the AC Mains/power supply cannot support all channels driven simultaneously at this level, which would require over 5,000W and only occur under a special test condition. The amplifier easily drives lower impedance loads."

Translation -- your house will run out of juice before your amp does.  Suffice it to say I think you're worrying needlessly over the power issue.  You have a beast of an amp. 

Hi Steve. The Triton's cannot and should not be bi-amped.

you should never run 2 center channels especially if one of them is in the ceiling.