The obstruction conjecture for strongly exotic H-slice trace surgeries

Let $K$ and $K'$ be knots in $S^3$, and let $S^3_0(K)$ denote the $3$-manifold obtained by zero surgery on $K$. A knot is H-slice in a $4$-manifold $X$ if it bounds a smoothly embedded disk in $X$ representing the relevant homological sliceness condition. Let $b^+(X)$ be the dimension of a maximal positive-definite subspace of the intersection form of $X$. Obstruction conjecture. If there is a zero-surgery homeomorphism

$$\phi:S^3_0(K)\longrightarrow S^3_0(K')$$

and $K$ is H-slice in a symplectic $4$-manifold $X$ with $b^+(X)=3\ \operatorname{mod} 4$, then $-K'$ does not bound a disk $\Delta$ in any symplectic $4$-manifold $X'$ with $b^+(X')=3\ \operatorname{mod} 4$, $[\Delta]^2\geq 0$, and $[\Delta]\neq 0$. The conjecture is intended to say that the Manolescu–Marengon–Piccirillo obstruction cannot detect strongly exotic H-slice trace surgeries; its status is not resolved in the supplied text.