As a piper, I think of all the tunes that would have and could have been appropriate. HOWEVER, 99.99% of America is made of of non-pipers who know only two tunes. AG by name and STB as "that bagpipe song". While not my favorite (although the first tune I ever learned) it was appropriate for the listening audience.

Now as far as tuning. Cold tuning should be (one of) the first thing a piper learns. If you spend a half hour playing and tuning, then put them down for fifteen to thirty minutes, you will be out of tune to one degree or another, depending on climate. The proper way to handle this is pick 'em up, play for about a minute and tune them. Put them back down and wait your turn. The reeds are still the same temperature and humidity as when you started. The other oprion is to play as long as you want, but have to sit there waiting, blowing softly into them the entire time. I prefer to not waste my breath.

If playing a long set, however, your best bet is indeed the "sit and blow softly" method. But for a couple stanzas of AG? Tune them cold and go get a Frosted Barley Pop.