"When all its work is done" definitely supports the ironic interpretation.
I intuitively read this more as taking a little consolation in the bigness of the truth relative to the petty little intrigues and dramas that distort it. I agree that for people with out values this is illegitimate, and I think it's kind of a stretch for the speaker, too, but I don't see them as being cannily ironic so much a grasping for solace; same tone you get from Marcus Aurelius when he reassures you than eventually you'll be dead.
I mean, I think the "plea for speed" is a normatively correct response to this situation, but it doesn't feel like what the narrator is doing; he's off nature-watching somewhere*.
(And writing poems- maybe a crux is that I feel like we're kind of supposed to ignore that part unless she calls attention to it? Actually, how closely are you identifying Patmore with the narrator, here?)
*Which is also very healthy, to be clear, and I don't mean to suggest I'd actually begrudge him that.
EDIT: Spelling
This is my favorite poem that's secretly about the necessity of revealing information about deception!
Here, in this little Bay,
Full of tumultuous life and great repose,
Where, twice a day,
The purposeless, glad ocean comes and goes,
Under high cliffs, and far from the huge town,
I sit me down.
For want of me the world's course will not fail:
When all its work is done, the lie shall rot;
The truth is great, and shall prevail,
When none cares whether it prevail or not.
Truth will win out in the end—after no one has any remaining incentive to lie, because the liars have already gotten everything they wanted? Is that supposed to be comforting? I'm going to assume the contented tone is ironic, and that this is really a coded plea for the importance of speed. The truth is great and shall prevail ... and the work of rationality is to get it to prevail faster—the need of us to make the world's course fail.