but I can't see how to change that path in File::Cache.

Both File::Cache and Cache::FileCache use the tmpdir() routine from File::Spec.  If you weren't running in taint mode, you could simply set the environment variable TMPDIR, but in taint mode, the variable is ignored. So, a quick hack around this would be to monkey patch Cache::FileCache's _Get_Temp_Directory() routine:

use Cache::FileCache;

{
no warnings 'redefine';
sub Cache::FileCache::_Get_Temp_Directory {
    return File::Spec->_tmpdir( '/home/username/tmp' );
}
}
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The directory must exist, i.e. it isn't created by the call. Also note the underscore in _tmpdir. This is the routine which is normally (internally) called like this $self->_tmpdir( $ENV{TMPDIR}, "/tmp" );