Not sure where you are placing the code as you don’t say – but you will need to edit the WordPress signup code / file and add your random string code in there and then hide the input for the sub-domain or set it to disabled and set it’s value to the random string.
You’ll then also need to encode the same random string in the form and check that the encoding is correct when the form is submitted so that you know it hasn’t been changed (it would be easy to change the random code in the HTML using something like firebug).
Once you get past the processing then the blog creation will be the same and antisplog will work as before.