Sorry – I missed that the OP mentions three of mine.
If you do include singing, there are lots of others, but the OP already discounts those.
One problem is that syndicated runs of shows tend to truncate the openings, so it’s not obvious (if you haven’t seen the initial run) that there ever was a spoken narration.
Did The Time Tunnel have an opening narration? I think so, but I don’t recall.
i think The Guns of Will Sonnett did, too.
How about The Land of the Lost?
“Marshall, Will and Holly
on a routine expedition
when the greatest earthquake
ever known…”
The Outer Limits
Royal Pains has one narrated by the main character.
3 that might have one, but I don’t quite remember:
Sliders
In Plain Sight
Now and Again (the one with Dennis Haysbert and Eric Close)
Project UFO, Ezekiel saw the wheel…
The Magician, All of the magic you are about to see…
In Plain Sight does, explaining how many people are in Witness Protection.
Leverage does as well (at least it did in the first season. Can’t remember if it still does.)
Only some of the seasons of JAG had a lead-in about how Harmon Rabb went from navy pilot to navy lawyer
“I’m just trying to be a better person. My name is Earl”
The current Lifetime series Drop Dead Diva uses a narrated intro to explain the convoluted premise (skinny model dies and comes back in the body of overweight lawyer).
Hardcastle & McCormick used a narration in the first season to explain its premise (Judge hires the last guy he convicted before he retired to help him go after criminals vigilante-style).
Each episode of Dragnet opened with a monologue by Jack Webb.
Sliders definitely did.
Didn’t Space:1999 have an opening narration?
I’m not sure I was really looking for a factual answer.