From memory, the HOME variable is populated from /etc/passwd. You could try just changing the entry in /etc/passwd if you wanted to manually move the files over. Alternatively, you could use:
usermod -d /multimedia/home/steqve -m steqve
This would move the files from their existing location to the new one.
I haven't tried this, but the following is from the man page for usermod (on Slackware 10.2):
usermod - Modify a user account
usermod [-c comment] [-d home_dir [-m]]
[-e expire_date] [-f inactive_time]
[-g initial_group] [-G group [,...]]
[-l login_name] [-p passwd]
[-s shell] [-u uid [-o]] [-L|-U] login
The usermod command modifies the system account files to reflect the changes that are speci-
fied on the command line. The options which apply to the usermod command are:
The user's new login directory. If the -m option is given the contents of the cur-
rent home directory will be moved to the new home directory, which is created if it
does not already exist.