Is a CHMOD 0777 not enough to give you move/delete rights?
If you are friendly with your sysadmin, or you are the sysadmin, you could make a crontab entry that runs every X minutes and chmod's all files in a certain directory to your user and group.
Then there is allways the nasty way....
!!Note, the following is something that no sane system administrator would ever let you do!!
Have a look at a program called "sudo"
this lets you define a number of root commands to become available to a number of users.
These commands will be executed as root.
You could make "chown" available to apache and with a little wrapped you could make it so that apache can only chown files in a certain dir to your name and group.