I'd appreciate if someone could sift through bands and find an Icelandic-Language Thrash or Death band...
Other genres are welcome of course, but try to stay clear of Folk metal. Thanks!

I've been through literally every Icelandic band, and as far as lyrics are concerned, 75% of them are in English, although there are indeed quite a few Icelandic folk/metal bands.

I'll give you most of them (as there aren't very many) although a lot of them have some folk in them. The ones in bold directly match your criteria:

Árstíðir Lífsins
Bootlegs
Dynfari
Forgarður Helvítis
Fortið
Munnriður
Potentiam (although mostly in English)
Skálmöld
Sólstafir
Thule

There's probably a few I missed, as it's been a while, but that should be most of them.

Thanks a bunch, dude!