= Solution
For a small opposing <force>, the relevant parameter is $q=\beta F\delta\ll1$. A <Taylor series> gives
$$
e^q-1-q=\frac{q^2}{2}\left(1+\frac q3+\frac{q^2}{12}+\cdots\right),
$$
so
$$
\boxed{j_0=\frac{2D}{\delta^2}\left(1-\frac q3+\frac{q^2}{36}+O(q^3)\right)
\longrightarrow\frac{2D}{\delta^2}.}
$$
In particular the zero-force rate is finite, despite the numerator and denominator of the original expression both vanishing.
For $q\gg1$, the exponential dominates the denominator:
$$
\boxed{j_0\sim D\beta^2F^2e^{-\beta F\delta}
=\frac{D}{\delta^2}q^2e^{-q}.}
$$
Opening a monomer-sized gap is exponentially rare at high opposing <force>. The algebraic $F^2$ prefactor belongs to this first-passage model and must not be discarded when quoting the leading asymptotic rate.
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