I've played with versions of this sort of thing here a couple of times before, but right now this new version of the sentence seems best to me (in terms of denying the paracomplete theorist escape routes that may have been afforded by earlier, sloppier versions):
Sentence S: An omniscient and ideally rational being would not accept this sentence.
If you take S to be true, you're committed to the uncomfortable claim that an ideally rational being would reject a sentence that they knew to be true. If you take S to be false, then you're faced with an unattractive choice between being committed to saying that (a) it's also true, or that (b) sometimes an ideally rational being would accept a sentence they knew to be false. If you take S to be one of those sentences about which a good paracompletist recommends rejecting the relevant instance of the Law of the Excluded Middle, then you are committed to saying that some such sentences are also true, which would seem to defeat the whole point of the paracomplete manuever of switching from making claims about truth-values to making claims about acceptance and rejection.
Moreover, S also seems to pose a big problem for dialetheists who lean on acceptance/rejection talk to get around their difficulties with the notion of "just false." (The problem, of course, being that for whatever formulation you use to differentiate false statements that are also true from other false statements, you can always construct a sentence that says of itself that it is in the latter category--e.g. "this sentence is just false and not true.") At one time, Graham Priest was in this category--in the first edition of In Contradiction, he claims that dialetheists, despite their rejection of Disjunctive Syllogism, are still entitled to a Disjunctive Syllogism-like rule of reasoning expressed in acceptance-and-rejection talk rather than negation-talk. In the second edition, he renounces this claim, and in Doubt Truth To Be A Liar he has an extended discussion where he says that good dialetheists should accept that the ground for rational acceptance might sometimes overlap with the ground for rational rejection. JC Beall, on the other hand, still seems to think that he can avoid this conclusion. In Spandrels of Truth, he uses acceptance and rejection talk almost as much as Field does in Saving Truth From Paradox and for many of the same sorts of purposes, for example saying that he thinks that Curry sentences should all be rejected. (Basically, it looks to me paracompletists want to use "accept", "reject" and "neither accept nor reject" pretty much exactly the way truth-value-gap theorists use "true," false," and "neither true nor false," but without running into the revenge paradoxes, and that dialetheists like Beall or the previous version of Priest want to use "accept" and "reject" as stand-ins for the classical behavior of "true" and "false." In either case, the psychological concepts are substituted for the semantic ones, so that one can have one's cake and eat it too in terms of one's preferred non-classical solution to the paradoxes.) These purposes, it seems to me, are pretty well foiled if it turns out that (given his committment to thinking that paradoxical sentences are meaningful, have their apparent truth conditions and so on) he has no choice but to admit that either (a) some sentences both should and shouldn't be accepted, or (b) some true sentences shouldn't be accepted, or (c) some sentences should be accepted despite failing to be true.