I imagine you could do it in PHP. May we see a cut-down sample of one of the SQL files? Is it a set of SQL statements that are semi-colon separated?
This script looks like it would work. It uses the
multi_query method in the MySQLi connector, which will save you the bother of writing PHP to parse your SQL into lines.
How long do they normally take to import? Try triggering your import script over the web to start with, but if this times out because the files are large, you might be able to do something with cron. Depends on whether you overflow the permitted storage size in MySQL for free accounts, I guess .