Sæll, Llama.

I don't really know the answers to your
latest questions. Yes, I think "láta + pp."
may be somewhat archaic/poetic in the way
it's used here:

"Ok Ellu bak,
at, lét, hinns sat,
Ívarr, ara,
Jórvík, skorit."

But note the difference in meaning

Hann lét bakit skorit. = He had the back cut.
Hann lét skera bakit. = He had SOMEONE cut the back.

We still use "láta + pp." in various contexts, for example:

Hún lét það ósagt. = She refrained from saying it.
Hann lét það ógert. = He refrained from doing it.

Kveðja,
Haukur