Yup, I love that one... just not enough else (if anything) on that double CD to get me to buy it. Along cheerful lines, I like 'Distant Melody' from Ballroom Desire (nice show length at 1m 55s), and not as cheerful I really like 'A Moment Lost' from Ballroom Fascination.
I sympathise with Pirate Smith about Story of Tina. When i was doing my silver medal classes in 1963, my teacher played "Singing Piano" by Victor Silvester every blasted week: diddly-DEE, diddly-DEE, diddly-DEE, diddly-DUM . . . drove me mad. The record came up on ebay recently and I bought it. It was 49p, and actually is quite a nice tune. I might even play it again in another 45 years time, if I'm still around . . . bit unlikely though.
Being partial to rock, in addition to those mentioned by others in this thread (Natural Woman, Take It To The Limit, Are You Lonesome Tonight), my list would include:
Beatles - Here, There and Everywhere
Byrds - Hickory Wind
Elvis Presley - Bitter They Are, Harder They Fall
Flying Burrito Brothers - Sin City
Jackie Deshannon - What The World Needs Now
Moody Blues - Go Now (a bit fast)
Wings - Mull Of Kintyre
I'm not aware of any waltzes by Lancelot Link and the Evolution - but I'll look into it.
if you want strictly instrumental and moving, I suggest Apassionata by Secret Garden, it's on a CD called White Stones, track no.9. Be warned, it is very slow, too slow for strict tempo. But boy is it melodic, moving, and extremely waltzable.