I rented this video about 8 years ago. I think it was a New Zealand or
Australian production. A guy fleeing someone else in a fast car has a
fatal accident but at the moment of death transfers into another
time/place/world. He gets into trouble there, too, so as a last-ditch
evasion ploy he tries to do it again intentionally -- hoping to return
to his point of origin; but instead he lands in another, even stranger
place.
What haunts me about this movie is its music, and the final scene with
its strangely alien but beautiful scenery.

[More than likely, not the answer]

That sounds almost like the premise
behind FreeJack (1992), close on the
timeframe.

Starring
Emilio Estevez ....  Alex Furlong  
Mick Jagger ....  Victor Vacendak  
Rene Russo ....  Julie Redlund  
Anthony Hopkins ....  McCandless  

http://us.imdb.com/Title?0104299

Filming Location:
Atlanta, Georgia, USA

Morgan Creek Productions (US)
http://us.imdb.com/List?production-companies=Morgan+Creek+Productions+[us]&&tv=on&&heading=18;produced+by;Morgan+Creek+Productions+[us]

I won't spoil the ending (because
everyone should see it at least once)
But he isn't trying to get back

-AI

Freejack (suggested by alienintelligence) also came to my mind.  The
premise of that movie is a person is stolen from the past, just before
they die, so someone in the future can have their body.  The movie
revolves around a race car driver who dies in a spectacular crash.

An alternative that matches several of the items you described,
especially the ending in a stranger place is "Quiet Earth".  It is a
1985 New Zealand "Last Man on Earth" film.
http://us.imdb.com/Title?0089869

The original music was done by John Charles.
http://us.imdb.com/Name?Charles,+John+(III)

This page includes an image from the movie (which you might recognize
the image) and sample audio from the CD.
http://www.nzvideos.org/quietCD.html

There may be other sources of the CD.
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&q=%22quiet+earth%22+%22john+charles%22
http://cgi.ebay.com/ws/eBayISAPI.dll?ViewItem&item=893129486

This is evergreen, adding a comment. (Not sure if _this_ is the box
for questioner to reply, but can't find guidance, so here it is)(And I
still don't understnd why everyone -- including me -- seems to be from
_Georgia_ [ga suffix]!).

alienintelligence, thanks for your input. It _is_ in the ballpark, but
I would have remembered such a stellar cast.

ulu, I was 99% sure you'd got it: "Quiet Earth". The title rings a
bell, and I was sure it featured actors I didn't know and was produced
in another Anglo country. I followed the link to the soundtrack album
cover. Its illustration showed the same unusual cloud formations that
had intrigued me when I'd seen the film. That was the clincher.
(Unfortunately I can't listen to the sound sample, as my sound
facilities are down at present. But I'm really looking forward to
doing so later!!)

I'm very happy with the information and am now closing the question.