When I say that you need to set the character set on the database, I mean with an SQL command like this:
ALTER DATABASE your_database CHARACTER SET latin1 COLLATE latin1_swedish_ci;
(replacing this with the appropriate character set and collation for your existing data)
.. if it gives you an error when executing this because of permissions, let us know in a support request, and I can try doing it for you.
I don't know where you would set the character set in your specific app (every one is different), so this is something that you would have to try to find by looking in its configuration files and/or documentation. If it's a well-written application, changing the setting will cause it to perform the command "SET NAMES ..." first whenever it connects to the MySQL server.
It is possible that you might also need to use a different workaround that I'm not familiar with. Character sets and collations and converting between them is a rather complicated subject. A Googling turns up many others who have had similar problems to yours, and the general consensus seems to be that switching to udf8 throughout is the best plan in the long run -- but that can be a rather involved process, which is why I was suggesting the workaround of continuing to use your existing set. Before you continue, it would be worth checking out some of the articles out there on character set problems.