I decided I had to change all the collations on the databases and tables.
Using phpMyAdmin, I ran the command
show databases
Then I copy the results to Textpad and use the following regular expressions:
# ^([^#^\n])(.*)\n => \1\2\n\n
# ^([^#^\n])(.*)\n => ALTER DATABASE \1\2 COLLATE utf8_general_ci ;\n
Similarly for each table in each database:
show tables
# ^([^#^\n])(.*)\n => \1\2\n\n
# ^([^#^\n])(.*)\n => ALTER TABLE \1\2 COLLATE utf8_general_ci ;\n