I was beginning to think I'd never get to this but, finally, I did. So, I thought I'd share my experience in case it case it might prove useful to someone.
First, Garvin got my situation a bit backwards. I needed to move
FROM PostgreSQL
TO MySql. Not a common migration, judging from my Google searching. Also, I had shell (including root) access to the source machine (my home Linux box), but only FTP and phpMyAdmin access to the intended target.
I began with a flash of inspiration. Since I had to convert the data at some point, why not do it where I had the better access? So, I did a backup dump and upgraded my home system to v0.9.1. (Outstanding upgrade support, by the way. The two-point upgrade from 0.7.3 went without a hitch.) Once I was certain the upgraded installation worked, I did another dump and started using the table creation commands in the Postgres dump to build the tables on the target through phpMyAdmin. I got a litte concerned about my ability to translate between Postgres's database structure and MySql's. (E.g., Postgres implements auto-increment fields as a sequence plus a DEFAULT setting for the field that generates values from the sequence; MySql doesn't have a bool type; there were lots of specific constraints in the Postgres dump, and I couldn't figure out how/if they would translate to MySql; etc.) After some time I thought I'd have a go at letting S9Y build the MySql tables for me. So, I installed it on the target and let it do just that.
So far, so good. That set up the framework and non-content tables. Now I was left with migrating my blog entries and related data. By having Postgres dump the data as INSERT statements instead of its default COPY commands, I was able to copy and paste them into phpMyAdmin's query text box, for the most part, verbatim. I had to remove the double quotes Postgres places around field names that match key words, such as "type" and "path". When I forgot, phpMyAdmin was happy to remind me.

Multiple INSERT statements can be pasted and executed at a time, so the process didn't take very long. Since S9y's installation creates a user, I manually edited the author table (I only have two entries) to match the values from my old installation instead of using the dump directly.
My migration was made easier by the fact that I didn't have very many blog entries, but with sufficient care I don't think this would be an insurmountable task even for large databases. In general I was careful that record ID values weren't changed during the migration, but these values are part of the data dump so it was not difficult to do. If your migration gets hopelessly bodged you can just drop all the tables and start over.
Thanks to Garvin for his quick reply (even though it languished for a few months) that give me a handle on how the task might be accomplished, and the sense that it was even feasible.