My preference is for an ordinal approach to phenomenology - one that attempts to move past the sort of Kantian finitude Husserl maintained by relegating the real to first-person conscious appearances. The ordinal phenomenological approach, by contrast, involves the twin notions of ordinality and ontological parity. I've already discussed how Peirce, Buchler, Hartshorne, and Whitehead offer radically different phenomenologies than the sort of (Kantian) transcendental phenomenology that one finds in Husserl.
The most pressing question is this however. Is the reduction made by human consciousness as an act intended for human consciousness essential to the phenomenological method? Perhaps the question ceases to be interesting or even relevant because phenomenology rarely goes beyond trying to decide what phenomenology is exactly as a method (something Husserl could never move past it appears). But it would be insular to suppose that phenomenology means Husserl or perhaps even means reduction.
A better question might be: for phenomenology do method and "objective" correlate (*what* so to speak is the content of analysis) follow each other all of the way down? Or is it possible that whatever content to be described exceeds the consciousness attempting to describe it? If phenomenology is properly made speculative (mathematized or turned logically modal or categorical, as in Peirce, Buchler, Hartshorne, et al), then speculative realism's ontological demonstrations are capable of becoming epistemological descriptions. (If speculation is a demonstration of "what can be" rather than of "what is" - pace Q. Meillassoux - then the demonstration of what can be, a modal categorical (phenomenological) determination, would reduce to epistemological description in its value for any possible observer yet retain realist metaphysical element - but such is not *presupposed* in the phenomenological method).
Moreover, if the qualitative, or "present to" first-person or subjective conscious experience component is supplanted by modal-categorical revelation so as to maintain an adequate level of objective demonstration and metaphysical realism, we need then only ask how does such an approach regard the conditions for consciousness which enact method. In other words, how are the categories of cosmos isomorphic to the consciousness that happens to be rendering them. Note that this isn't the other way around (moving from categories of conscious experience to cosmos, which was the Kantian-Husserlian transcendental mistake).
In the sense that, given a speculative phenomenology is possible but only by re-conceiving its method in modal-categorial terms, perhaps the "experiential" component of phenomenological analysis - a natural self-disclosure of sorts - could be preserved in its extrahuman (inhuman) elements despite the elimination of its qualitative or first-person "present to consciousness" viewpoint. Phenomenology, methodologically, wouldn't be the knowing-what of experience but the exhibition of the becoming-how of the real, a demonstration and then description of reality's possible becoming.
In any case, those are just a few thoughts on how phenomenology might in the future be able to be of some use for those interested in speculative realist philosophy.