Exactness of speculative sampling with a modified acceptance rule

Suppose an implementer changes the acceptance probability from $\min(1, p(x)/q(x))$ to $\min(1, \kappa\,p(x)/q(x))$ for a constant $\kappa > 1$, hoping to accept more often, and keeps the residual distribution $p'(x)\propto\max(0, p(x)-q(x))$ unchanged.

1. Prove that the resulting sampler is no longer exact, by computing the output distribution.
2. Determine the total variation distance between the output and $p$ for the two-point example $p = (0.6, 0.4)$, $q = (0.5, 0.5)$, $\kappa = 1.5$.
3. State the general principle the failure illustrates.