OK, here's my solution for manually moving the numbering on split; the
reason the numbering wasn't visually centered is because the top and
bottom lines of the split equation are diff. heights. So you trick
latex into thinking they're the same heights by appending, to the
first line, \vphantom{TALL MATH}, where "TALL MATH" is arbitrarily
chosen to be a math expression with large vertical dimensions --
comparable to those in the second line. But then you have to
compensate with \\[-(some no.)em]. And if you are using these
commands, you also need to append \notag to each -- otherwise you get
mutltiple equation numbers overwritten on top of each other (the same
applies for adjusting vert space around \intertext, see below). So
there's a lot of manual adjustment, which is not ideal if you have
many equations of this form.
The nicest thing would be to use align, but there seems to be an
incompatibility between it and \tag that I've not been able to
resolve.
Again, note that you need the amsmath pkg to compile this:
\begin{gather}
\begin{split}
E(d;L)&=E_{\text{int}} +E_{\text{bend}}
\vphantom{\int\limits_{\int}^{\int}}\\
\\[-2.8em]
&=\sqrt{3} F_o (c^2+cd)L\exp (-d/c)+\frac{4\pi \xi k_{\text{B}T}}
{\sqrt 3 d^2}\int\limits_{R_{\text{in}} }^{R_o } {dr} \frac{\sqrt
{R_o^2-r^2}}{r}\text{,}
\label{eq:salt3}
\end{split}
\\[-2.2em]\notag
\intertext{with}\notag
\\[-2.7em]\notag
R_{\text{in}} =\sqrt{R_o^2-\left(\frac{3 \sqrt{3} d^2 L}{8 \pi }\right)