Believe it or not, an easy one I like to bust out when I am around a piano (and it's late and we are all drunk) that for a beautiful and slow melody would be "Suicide is Painless". Theme song from M.A.S.H! Easy chords, recognizable melody that offers plenty of opportunities for variations and extensions.
Maybe don't sing the lyrics for them.
If you're willing to supplement melodic vocals with some arranging, Vienna Teng is great (Say Uncle and Between are two of my favorites).
The Dead Island theme is piano driven, with strings on top of it. With some creativity, you could make it work.
I've fiddled with a solo version. Same deal with the more popular themes from:
- The LOST soundtrack
- Life and Death
- No Place Like Home
Others have suggested I try Einaudi. Primavera is worth looking into. It isn't the slowest, but it's simple, and lends itself well to expressiveness.
Pavane Pour Une Infante Defunte remains the prettiest piano piece ever fucking written. I know you said no classical, but there it is.
Also, a lot of Morricone would fit well here. Look at La Califfa and Gabriel's Oboe in particular.