HTML: is it possible to provide an alternate document title?

You can't use aria-* attributes on <title>. See ARIA in HTML:

No role or aria-* attributes

Original answer

According to MDN the <title> element supports only global attributes (they include aria-* attributes) but I think it is not supported by most screen readers.

Accessibility inspector viewing page with this (see below) <title> element in Firefox shows “a” in the document name field so Firefox does not support alternate document titles.

<title alt="b" aria-label="c">a</title>