Burt Bacharach, “Anybody Who Had a Heart” and “Make It Easy On Yourself”.
Find the Edwin McCain cover, if you can. It’s marvelous.
I recommend “One Step Up” by Bruce Springsteen, NOT the album version (which isn’t very good at all), the live/acoustic one.
How could I have forgotten “At This Moment” Billy Vera-also performed by Tom Jones
“Love on the Rocks” Neil Diamond while I’m thinking lounge singers.
Trout Fishing in America has a song called “You Can’t Get There from Here” about a long-ago relationship that includes these lines:
“I’ve got a box of old photographs
And every image came true
Funny, they almost told the future
See I’m not in the picture with you.”
Good song.
My girlfriend of the last six years and I just broke up and I’ve been wearing out Warren Zevon’s “She’s Too Good For Me”, “El Amor de mi Vida” and “Please Stay”.
After cbawlmer’s post, I’m thinking that I really like Ringo Starr’s “Photograph”:
“Everytime I see your face,
It reminds me of the places we used to go
But all I’ve got is a photograph,
And I realize you’re not coming back anymore”
“Blond in the Bleachers” or “Help Me” by Joni Mitchell.
And then there’s that Broadway show-tune staple “50 percent of him” - the anthem for desperate codependants everywhere.
I came in to nominate this song, but can’t believe that people sing this song at weddings?! Do they also sing Give My Love to Rose because it has the word ‘love’ in the title? 
Watching Alice - Nick Cave & the Bad Seeds
Oh yeah, “Here Comes My Baby” by Cat Stevens.
Northern Sky by Nick Drake.
Astonishingly wistful.
Sigh.
The song I’m thinking of is, maybe, “The Last Song” by (I think Edward Bear).
Some of the lyrics go like this, whatever it is:
It’s the last song…I’ll ever write for you
…
You’ll come looking for the light and it won’t be there…
But I looove you, oh, Yes I do!
…etc.
Really heart-tugging.
I thought of a few more:
“That’s The Way” by Led Zeppelin
“You’ve Got To Hide Your Love Away” by the Beatles
“Saw Red” by Sublime (the acoustic version)
I’m not familiar with the songs the OP uses as examples, if he could give some more well-known examples (possibly of songs from this thread) that matched what he’s going for that would be helpful.
Also the famous “Girl From Ipanema” matches the OP’s description, lyrically at least, to a T. I don’t really know whose version of that song is definitive though.
Macarthur Park
MacArthur’s Park is melting in the dark
All the sweet, green icing flowing down
Someone left the cake out in the rain
I don’t think that I can take it
'Cause it took so long to bake it
And I’ll never have that recipe again
Oh, no!
Oh, no!
No!
Oh, no!!
Diary, David Gates & Bread
"The love she waited for was someone else…not me.
“You Always Hurt the One You Love” by the Ink Spots or Mills Bros. is a bit more of a general hurtin’ love song, but it’s nice and mellow.
“Solitary Man” by Johnny Cash or Chris Isaak (don’t kill me, but I think I may prefer the latter version)
Most Ink Spots songs kinda fall into that category. Another especially good one from the group is “Maybe”.
Earth Wind and Fire’s After the Love is Gone
Something’s Always Wrong by Toad the Wet Sprocket
I Can’t Make You Love Me by Bonnie Raitt
I immediately thought of “That’s as close as I’ll get…” by Aaron Tippin.
“New Orleans” by Cowboy Mouth.
I can’t believe nobody has yet nominated “Love Hurts” by Nazareth (OK, maybe not smooth enough for the OP) and “Nothing Compares 2 U” by Sinead O’Connor. Two classic tunes.
Slightly tackier, but still a reasonable pop song that qualifies is Atomic Kitten’s “Whole Again.”