Can reversible reactions proceed by different mechanisms in the forward and reverse directions? It seems odd to me that this would be the case, but it also seems odd that it wouldn't.
Imagine a mechanism for a (forward) reaction that includes a slow reversible step and a fast irreversible step:

$$
\begin{align}
\ce{A &amp;&lt;=&gt; B} &amp;\quad &amp;\text{(slow)} \\
\ce{B &amp;-&gt; C} &amp;\quad &amp;\text{(fast)}
\end{align}
$$

If the second step is irreversible, it's presumably going to be highly unfavorable to run in the reverse direction, and so there ought to be some alternate mechanism with a lower $E_\mathrm{a}.$ Is it possible that the reverse reaction is more favorable by a different mechanism? If not, why not?
Yes, you can. An ideal Carnot cycle (admittedly not a reaction) illustrates how this is possible. In such a cycle each step is reversible. To return to a state you can either reverse the direction of the process (running say a heat engine as a refrigerator) or follow the full path of the cycle until the state is again encountered.