There used to be an all-Soul HD station down here (since replaced) that was the only thing worth listening to on FM.
Upon hearing this, the vocals were so powerful I had to look her up…
If we’re going to include music from the early sixties, I’ll nominate Hello Stranger by Barbara Lewis.
Some real good ones here, but you’ve got to include Cruisin’ by Smokey Robinson.
Well, pretty much anything by Smokey Robinson. 
So, several years ago, I did a project where I went through the top 100 songs each week, starting with 1970. (I started with Billboard, many issues of which was digitize on google books), listened to them on youtube, and added the ones I liked to a couple of youtube lists.
(Sadly, youtube will delete videos without leaving any metadata, so half of these are gone. Which is why I’m doing this project again)
So these two lists aren’t exactly what you are asking for? But the first one is all 70s, and there might be some more obscure hits on there in the vein you’re looking for.
The second one is not reliably 70s, but mostly so.
Missing on the second one is Bill Withers - Use Me which I don’t even remember from when I was a kid, but loved at first hearing during this project.
And f you reach back into the 60’s, you can’t leave Sam Cookeout of the mix.