Boundary slopes (nearly) bound exceptional slopes

For a hyperbolic knot in $S^3$, Dehn surgery along slope $r\in \text{Q}\cup \{\frac{1}{0}\}$ is {\em exceptional} if it results in a non-hyperbolic manifold. We say meridional surgery, $r=\frac{1}{0}$, is {\em trivial} as it recovers the manifold $S^3$. We provide evidence in support of two conjectures. The first (inspired by a question of Professor Motegi) states that there are boundary slopes $b_1<b_2$ such that all non-trivial exceptional surgeries occur, as rational numbers, in the interval $[b_1,b_2]$. We say a boundary slope is {\em NIT} if it is non-integral or toroidal. Second, when there are non-trivial exceptional surgeries, we conjecture there are NIT boundary slopes $b_1\le b_2$ so that the exceptional surgeries lie in $[\text{floor}{b}_1,\text{ceil}{b}_2]$. Moreover, if $\text{ceil}{b}_1\le \text{floor}{b}_2$, the integers in the interval $[\text{ceil}{b}_1,\text{floor}{b}_2]$ are all exceptional surgeries.