Of the 8 McIntosh amps I have owned, none have been harsh no matter what.
Anyway, I have actually heard an MA6900 on Cornwall III. I have also heard the new MA6300 on Cornwall III. Both used Pioneer Elite source in the same large room and were fantastic with a slight improvement going to the 6900 because of its more laid back and round nature. The 6300 is a fantastic amp with better dynamics than the 6900 but slightly "harder" too - something the Cornwalls made fairly obvious. The 6300 was a better match with B&W 805S (wonderful combination BTW).
As for the room, I agree with the others that it might be a bit small for Cornwalls. They don't have very deep bass despite their size but they will produce enough energy at 40Hz to cause you problems in 13x13 room.
Unless of course you don't really care about neutrality and love lots of bass. In that case, go for it and see what you think.
The other exception would be if your room has permanent openings into adjoining rooms. If that is the case, you might be able to get away with it just fine. My room is 14x13 (17 meter square) but with two open doorways in the back corner; my speakers have the same bass extention specification as the Cornwall III, and my bass measures and sounds incredibly even, all things considered.
The Cornwall III are amazing speakers for the money. I was very highly impressed. I wanted to hear them on the MA2275 but wasn't able to. My feeling is they would be best with tubes but the 6900 is probably close enough. That integrated (and MC202 amp) is the most "classic tube" sounding SS amp I have ever heard. It makes the MC275 sound like modern hifi by comparison.
Arthur