>> After checking with Mazda,
>> they now think it's the ignition coil pack, which is on order.
>
> The '99 coil packs are known problems . I think it's likely your dealer has
> identified it properly. Let us know how it works out.

It looks like the problem is finally resolved, and it was the coil pack.
However, it took a while for this to become clear. A few hours after the
dealer replaced the coil pack, the check engine light came back on, but
without the roughness that I had experienced earlier. It turned out that the
catalytic converter had to be replaced again, because the ignition problems
with the bad coil pack ruined the cat (for the second time).