Unfortunately, I’m not sure there’s any way to override the use of /tmp here. I dug into the mod_fcgid source, and it’ll always store its files in the directory returned by apr_temp_dir_get(). On Linux, I’m pretty certain that’s always /tmp.
If you don’t mind some decrease in performance, you can ask Support to switch /tmp on your VPS to be stored on disk instead of tmpfs. That’ll let you store more than 128 MB of data in there.