Best amplification for Magico S3 newer version on your experience

Depending on your budget I agee Coda makes very good underappreciated amps. They fly below the radar. Your room isn't that big  too but  high amperage they put out is rather robust. That helps with the lower listening levels. A #16 would be magnificent. (I too have the s5.5 and it is amazing) Good luck making those Magico's sing.

I imagine your Magico dealer has multiple amps comparable to the CH, Solution, etc. level amps and would be tickled to death to lend you one which would allow you to compare them to your very-capable Luxman. 
My guess is that your Luxman will do extremely well when compared to those 5 figure amplifiers.  Please let us all know your experience!

You could also try the Anthem P2 amplifier for around 5k

It has plenty of power and will easily go down to 1 ohm

I have heard Magico with less than top of the line audiophile electronics and they sound terrible to my ear. The Magico are so detailed and fast that any imperfection in the signal path will get amplified. You want to be using top of the line electronics that are of your musical inclination. VTL, Audio Research, Boulder, Burmeister… this level.