I never heard of 4AD until I was handed a sample disk a few years ago. Probably at a music festival or something. Some of the bands I liked that the OP might want to check out:
Camera Obscura
The National
tUnE-yArDs
I’d also recommend going to NMEand Pitchfork.com for recommendations.
Based on your list, I think you might like Jesca Hoop. Here’s two of her songs to get you started:
Check out Martyn Bennett? Here’s his amazon.com page. Here’s his site. Here’s some songs to check out some are more traditional than others.
Scotland (From the Transatlantic Sessions)
Sky Blue Martyn Bennett mix (He was signed to Peter Gabriel’s record label, and Gabriel gave him the song to rework.)
Swallowtail
Erin That is a plumbing pipe didgeridoo he is playing there!
Karabach
Nae Regrets This ends up being a bawdy syncopated waltz!
While I recognize most of the bands on the OP’s list, they’re not my favorites. But I might be able to pull a few songs from my monthly recs that are similar enough…
Starting with other songs by a couple of those bands:
Doves - Kingdom of Rust
Doves - The Last Broadcast (Magnets Remix)
Elbow - Neat Little Rows
Elbow - The Bones of You
Other stuff:
Editors - Blood
Boy & Bear - Feeding Line
Kid Dakota - Ten Thousand Lakes
Seabird - Don’t You Know You’re Beautiful
Shearwater - Breaking the Yearlings
Low Duo - No Happier
Motorcycle - As The Rush Comes (Gabriel & Dresden Remix)
Nerves Junior - As Bright As Your Night Light
Metronomy - She Wants
David Bazan - Wolves At The Door
City & Colour - Fragile Bird
Dead Snares - City Sparks
Dirty Projectors - Stillness Is The Move
Niki & The Dove - The Fox
Tuó - Walk With Me
Kanute - Tangle Me
I Might Be Wrong - Elliot
Loch Lomond - Wax and Wire
An update:
timid1: Tokyoidaho’s Deep Canyons was beautifully engineered with a luscious sound. Still, I must say it wasn’t my cuppa.
don’t ask: I had never seen Music-map before. As you say, it’s lotsa fun. And, surprisingly complete. Even more unexpected (for me, at least) was that it was actually pretty accurate (with a few, WILD exceptions - Barry Manilow??!!:D)
[the next is out of order]
pookah: Fever Ray is, again, really nicely engineered with a stellar sound quality but, what can I say, it’s just not to my taste. Or, phrased differently, I did like it; it’s just that it didn’t get me excited. I didn’t think it was really outstanding.
[back in order]
phreesh: Thanks so much. That must have taken a huge amount of time. I really appreciate it. I didn’t listen to all your suggestions, but so far can say the followng:
Broken Bells, The High Road - very nice. Loved the ‘sound’ (and the quality). But, not quite a five-star track. More like a solid four (which is great!)
Caribou - I know and like their Andorra. That said, and although I loved the rhythm and percussion in Sun, it didn’t grab me the way a great track does. It was okay.
Morcheeba - what can I say? I know them, I love them. You knew, you sly devil, didn’t you!
Phoenix 1901 - ditto above. Know them/it, love them/it!
Yo La Tengo - a hat trick!! ditto, ditto , above. LOVE them.
Polyphonic Spree (Hanging Around) - what can I say? This is simply lovely A winner!
Gary T
I absolutely love Shivaree - you were spot on!
Sleepwalk (Santo & Johnny) - what can I say? What can anybody say? A classic!!
Sandie Shaw (Girl Don’ Come) - never heard this/her before. Powerhouse voice. I need to hear more from her before saying anything else.
Derek Webb (Blood of the Lamb) - WOW!! Yet another one I’d never heard/knew about. GREAT cut! I like it a lot. Thx!
Joan Jett (I Hate Myself) - sorry, . . .
newcomer:
Metric is amazing. Just awesome! How could I not have known them? I just listened to Synthetica (at their site on SoundCloud) and thought every track was stunning. That said, ‘Speed the Collapse’ was just spectacular! What a band!!
More to come . . .
(in the meantime, I’ll say, again, THANKS!)
This is kind of a cool site for finding new music. They tend to have some more obscure recommendations.
newcomer: And so is Yeah Yeah Yeahs (It’s Blitz) - Amazing. The whole album fantastic! I like your tastes!!
More to come . . .
Me pleased 
Special treat then - http://www.youtube.com/watch?v=cgjXp3fIFLI