Likely culprit for harshness at higher volumes?

Your Adcom is having difficulty with transients. The poorer the recording, the more apparent this becomes. Try a really good one like say, Lyle lovett's "Natural Forces" or Jimmy Roger's "Allstars", or Ray Charles' "Genius Loves Company". A really good amp won't be limited by the recording in that it will simply reproduce what's there accurately. So if the information is diminished, it won't attenuate that upper mid-range already attenuated in the poor recording we're all familiar with as "harshness". The recording will simply be apparently "lacking". If a great recording eliminates the issue, you need to consider the perfomance of your amp. All KEFs are great speakers regardless of there particular shortcomings. If it hurts or is bothering you that much, it's the amp.

That's just it. It's not the good one that reveals the amp's true potential nearly as much as the poor one. The amp is the heart of the system. Once you've gotten used to the attributes of your other gear, you then begin listening to, guess what?... your amp, "again". The component you get used to the quickest is believe it or not actually the weakest link, your speakers. What you will never get used to are the shortcomings of your amp because they are constantly being revealed and so become your focus. For the amp to "disappear", it needs 3 attributes relative to your ears; it has to be "fast", it has to have a truly flat frequency response- one that is not can seriously contribute to the harshness you're talking about, and it must be very linear. Whatever other attributes it has are a bonus A truly high-end amp is probably the one that leaves you scratching your head wondering what makes it a high-end amp because it's so "flat and dry". Everyone out there building amps is applying their own brand of "voo-doo" in order to compete with each other. What I mean by that is it's easy to show a flat response on a 6 inch tape. Stretch it out 3 feet and you'll see just how flat it really is! It's not possible to add without subtracting, and they're all doing it fooling you into thinking you're getting a superior product. It's usually located in the bottom end and/or upper mid-range- it being the most bothersome since it thickens transients in the vocal range which can be fatiguing or downright ear-piercing. At first it's an up front in your face soundstage but then begins to take it's toll on your ears with lots of missing depth. Poor recordings should simply sound as they should.."lacking". They should not be ear-piercing or irritating at all! Remember, the entire system is nothing but a playback device. If the components are of sufficient quality and functioning properly, "revealing" poorly embedded information should sound as smooth and clear in terms of what's there, as the opposite. It doesn't "improve" it, but just plays it back.DC offset problems and bias issues can definitely cause the problem you are experiencing. Are both channels the same temperature within a couple of degrees? Have you checked the offset? These factors can ruin the sound of an otherwise great amp.

Check temp at idle, not while playing music since program material varies from one side to the other. Let it sit for an hour. DC offset is easy. You need a multi-meter. Preamp set on anything other than phono, volume at o, speakers disconnected from amp. Set your meter at 2v or preferably lower if possible, ie: 200mv, probes on speaker terminals, red on pos, black on neg. Ideally, it should read o. Anything up to 50mv is acceptable, however any decent amp should be in the 20mv or lower region on each side. It's okay if they vary within this range. A fast amp is going to have a rise time of at least 1.5u seconds(micro-seconds), and a slewing rate of at least 40volts per u second. Linearity has to do with timing of each frequency as it reaches your ears. Flat response is just that, equal amplitude of all frequencies. Not all amps' DC offset is adjustable. Some have potentiometers for this purpose in which case it is, some have DC servo circuits, and some have discreet components that control this, in which cases it is not. Without experience, I would not attempt to adjust, but simply check and double check. If it is suspect, and typically could very well be, you need to take it to a reputable tech and have it looked at. O DC offset results in a voice coil resting where it should, in it's mid position. The farther off it is, either + or -, the more distortion the speakers will produce. Most amps have potentiometers to adjust bias or in other words, quiescent current. This procedure is more involved except to say 150ma is optimum per ch.. TNT audio has a great article on this which I've read and followed. Just Google "adjust the bias of your amp". I currently have some Bedinis, Ampzillas, Leach Low Tim, and Meridian amps. They're all great amps, but the best of the lot are the Leach amps. Interestingly enough, they are the ones that have no vested interest to compete and they are the only amps I've heard that "disappear".

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.