How Do I Let PHP Scripts Write To Files Without Making Them World Writable?

The webserver runs as user www, as will your php scripts.
You can give just user www permission to write to a file or direcotory using extended acls (access control lists).

This will give www write perms to a file:

setfacl -r -m user:www:rwx filename

To see what extended perms are on the file, you can use the command:

getfacl filename

You'll see a list like this

# file: dispatch.file
# owner: kim
# group: them
user::rwx
user:www:rwx #effective:rw-
group::r-- #effective:r--
mask:rw-
other:---

The webserver can then write to the file.
(But so can everyone else running a php script, because their scripts will also run as user www!!) But regular users should not be able to write to it.