> daiva is often equated with prārabdha-karma (pūrvajanmakṛtaṃ karma tad daivam iti kathyate, ityādi). Do we know?

As far as the Mokṣopāya is concerned, we do.

> from a radical non-dualist perspective, saṃsāra in its entirety, including cause and effect, karma and phala, etc, is illusory. Is that the perspective behind the Mokṣopāya's rejection of fate,

No, although the author (“Vasiṣṭha”) would subscribe to non-dualism from a purely ontological angle.

> or is the argument made on the level of 'conventional truth'?

The retributive causality of karma operates on the empirical level of existence, although within a certain framework only of principles that manage our present universe. Karma is part of it.

There are, to be sure, parallel universes, each created by individual creators (brahmā, virāj, etc.), who are unaware of their adjacent equals. The “natural laws” governing those alien universes are unpredictable. They depend entirely on the fancies of their originators, on the very first ideas that befell those Brahmā-s the moment they started to identifying themselves as “creators”.

As a consequence, Vasiṣṭha entertains the idea of parallel universes, where the natural laws known to us do not exist as we experience them here, as they possibly did never occur to their creators in the same manner. Thus, karma is restricted to our universe, because we cannot know anything about the respective situations prevailing in our neighbouring universes.

Apart from this limitation from a broader philosophical perspective, the crucial point from the empirical viewpoint of karma operating in our own universe is this:

daiva is the result of past actions (pūrva karman). Past actions are ultimately past efforts (pauruṣa). As efforts, past and present efforts do not differ in their nature. As they do not differ, it is possible to conquer the results of past actions by stronger counteractive measures (para-pauruṣa) of today. Therefore, past karma can be overcome by human effort. It is not inescapable. It cannot be  predicted by daivajñas as they cannot know the efforts a human might or might not be willing to take. For, it is a matter of free will, and that is also a matter where the whole topic becomes really interesting.

The idea behind the criticism of daiva in the Mokṣopāya in a nutshell: Fatalists consider and present themselves as victims of fate. It is a lame excuse, for actually they shy away from taking control of their own destiny by making efforts. Thus spake Vasiṣṭha.

Enjoy.