> Is not an unvoiced r merely a flapping of the tongue against the
> roof of the mouth by means of the flow of air alone in the absence
> of any vibrations emanating from the throat?

Yes.

> If this is the case,
> then the vowels i (within 'virki') and the e (within 'skerpa') must
> be VERY quite (even nearly inaudible).

This has never occurred to me nor have I seen it mentioned before.
There is certainly a full contrast of vowels before unvoiced r.

If you want to support your theory you can try listening to some Icelandic.

http://www.library.wisc.edu/etext/Jonas/Dalabondi/Dalabondi.html

The title, "Dalabóndinn í óþurrknum", contains an unvoiced 'r'.

> You Icelanders seem to tend to speak towards the front of the
> mouth (something like a Dutch speaker) - relative to a German
> or even an U.S. American which would lend itself towards an unvoiced
> r sound. Then again, I really don't know.

Neither do I.

> I've noticed what may fit the description of a half-voiced r in
> instances where one of us Yanks attempts to mimic an Indian accent. One
> starts with a nice voiced r that is allowed to suddenly cut out and
> leaves the tongue flapping owing to its own momentum. Is this, perhaps,
> what you mean?

I don't know. When I try to mimic an Indian accent I try to
make retroflex sounds.

Kveðja,
Haukur