Eggcorn Forum

Although this google Ngram indicates that self-referential is hugely more common than self-reverential and probably predates it too (thus reinforcing the impression of the former as acorn of the latter), I must acknowledge that most examples of self-reverential I found in my online sampling were either clearly meant to refer to actual self-reverence (not just self-reference) or ambiguous in that respect. I did, however, find a few examples that seem to point to self-reverential as an eggcorn of self-referential:

In the case of “Jurassic World,” you mount a self-reverential sequel laced with allusions to earlier episodes in which you even go so far as to point out how dinosaurs don’t capture people’s imaginations to the degree they once used to.
movie review

As Scream’s Randy Meeks, the dorky, motor-mouthed one who gives the film its self-reverential running commentary, so helpfully explained, if you want to survive in a horror movie then you have to abide by three essential rules…
another movie review

...his eventual performance of ‘Mexican Radio’ is not as inspired (who can blame him?) as the rest, and I would have preferred how i saw it back in ‘06: a tex mex rendition, implying a sort of self reverential nostaligia for the song and the period it was from…
review of a live album by the great Stan Ridgway

Even better, one of the more recent selections, the sweetly self-reverential “Old Habits Die Hard,” proves Jagger can still muster genius when required with a snap of his skinny fingers.
record review

Fans of Aaron Sorkin’s rapid-fire dialogue, self-reverential monologues and broadly drawn female protagonists will get every quip, demand, aside and traveling camera shot in comedian Amy Schumer’s “Newsroom” parody clip, “The Foodroom.”
TV show review