Gary -- One point of explanation might help you with regards to the use of square waves for testing purposes, as opposed to the sine wave testing you're currently doing:
1. Sine waves are very useful in determining things like maximum RMS power output delivered into a load, the amount of both THD and IM distortion present, tube element dissipation levels under dynamic conditions, etc., etc. The problem is, sine waves aren't a very good replica of what the intended use of the amplifier is for -- amplifying speech and music signals, and in our case, primarily music signals.
2. Music is highly transient in nature -- not smooth, round, and slow like sine waves. It is fast, sharp, and dynamic. So knowing how an amplifier behaves under transient conditions is very important towards the end of accurately amplifying music signals. An amplifier can amplify a sine wave quite well, but still perform very poorly when passing a square wave. At low frequencies, an amplifier with poor transient stability can steal available power output, cause speaker cone "breathing", and in the worst cases, be quite destructive to the amplifier. At high frequencies, poor transient stability shows up as oscillations or "ringing" that distorts the whole of an overall transient signal by allowing the repercussions of one transient to interfere with the next transition, and so on. With music, this blurs detail information and impacts clarity of sound.
3. Square waves have an extremely fast "rise time", which therefore allows them to become an excellent transient test signal to see how well the amplifier can deal with a transient, at that it settles down immediately after a transient is presented, so it doesn't interfere with the next, etc. Quite simply, a square wave is the best steadily repeating test signal that is most like a music waveform, and can yield a wealth of information about how capable the amplifier performs under dynamic conditions. As you continue on with your audio projects, I would encourage you to add a square wave generator to your arsenal of test equipment, and study how they can be used to really enhance the outcome of your projects.
Dave