Likely culprit for harshness at higher volumes?

Left: 7.2mV; Right 13.2mV. Same reading with volume at -95db (minimum) and 0db (wasn't sure what you meant by 'volume at 0'). So, I'm assuming that the DC offset on my amp is acceptable, even though left and right are a little different?

I don't really have any idea how to measure fast and linear but I assume that's not something adjustable (w/out changing internal components?) so I have what I have. I'm not even sure how to adjust for DC offset so it's a good thing it's within the range you suggested. :)

Planning to order the Sony headphones recommended by almarg when I get the money.....

Volume at minimum. Yes, very acceptable. Without bench equipment you cannot get specs for speed, linearity or frequency response but the best way to check those aspects is with your ears. It's really those characteristics we're dealing with when we judge and come to a conclusion on how an amp sounds, hence my original suspicion your amp is having difficulty with transient performance, referring to it's "speed". The poorer the recording, the more difficult it is for an amp to reproduce especially vocal transients ie: s, z, ch, j, v. Probably because one of the main ways to describe a poor recording is compression when the transients become very fine and close together. This can result in some pretty harsh sounds when the amp can't deal with them effectively.

Try hooking up an iPod or other mp3 player via a mini plug to RCA cable and see how that sounds. It shouldn't sound a clean as your CD player, but might help to determine if the CD player is part of the issue. You could even rip some music in WAV format so that it's not compressed for a slightly better comparison.

Saru - I'm not familiar with your gear, but I am familiar with "humming and then patting your chest -- what should be a smooth sound is disrupted by unnatural vibrations"
In my case it was the simple fact that I was overdriving the room. I was putting too much sound (volume) in there, and the bass interferred with the midrange, mainly vocals.
I fixed it by changing speakers and putting acoustic treatments in the room. That distortion is a distant memory.
Since you have a $0 budget, I suggest that you put some bulk in the room to help diagnose the problem: Blankets, pillows, boxes of stuff, even an extra piece of furniture (cloth). If this helps or eliminates then you know what the problem is. Then you might look for more permanent solutions that look good.
The fact that you rearranged the room and added blankets and got improvement leads me to believe this is your problem.
But do remember that there are limits with any system. You won't be able to play as loud as you want.

Saru - One other thought that is quick and easy.
If your room has a door, try playing loud to where the distortion occurs and then open the door. If you are overdriving the room then opening the door may relieve some pressure. If the distortion is decreased then this may give an idea if this is your problem.
My room is 12' x 13' and opening the door has this effect.