One of the arguments given for dialetheism is that the paradoxes of self-reference, such as the Liar paradox and Russell's paradox, are most naturally regarded as dialetheias (both true and false). To avoid triviality, dialetheists must use a paraconsistent logic in which ex contradictione quodlibet fails.
However, in a sufficiently expressive system, such as natural language or set theory with naive comprehension, paraconsistency is not enough to guarantee nontriviality, because of Curry's paradox. The standard response seems to be to use a logic that also lacks the contraction/absorption law A → (A → B) ⊢ A → B, thereby blocking the derivation of Curry's paradox.
It seems to me, though, that discarding contraction also blocks the other paradoxes of self-reference. So once we are willing to do without contraction, is there anything remaining of the motivation for dialetheism coming from these paradoxes? Are there any semantic or set-theoretic paradoxes whose derivation does not require contraction and hence can still be argued to be dialetheias?