Oberlin's restricted projection conjecture in three dimensions

Let $t\in[0,3]$ and let $s\in\left[0,\min\{t,1\}\right]$. For a Borel set $A\subseteq\mathbb{R}^3$ with $\dim A=t$, write $\rho_\theta(A)$ for its restricted projection at angle $\theta\in[0,2\pi)$. Oberlin's restricted projection conjecture. One should have

$$\dim\left\{\theta\in[0,2\pi):\dim\rho_\theta(A)<s\right\}\leq\max\left\{\frac{3s}{2}-\frac{t}{2},0\right\}.$$

The conjecture is an analogue of Oberlin's planar projection conjecture for restricted projections in $\mathbb{R}^3$. It is known when $t\leq1$ and $s=t$, and when $t\geq1$ and $s=1$; the case $s=t/3$ is the paper's preceding proposition. The intermediate cases remain open.