I used paper filing. And for paper filing if one has already done FP code-3 (biometrics) then they usually do not require you to do it for 765.
My experience in past to expedite EAD processing are:
1. Paper file
2. Fee in form of Money order, which ensures that your case is ready for processing and does not have to wait till your check is cleared (if you send a check instead of money order).
3. Mail your form to their physical address to Augustine Rd. Dallas, TX by Fedex. The P.O. box address in Mesquite, TX is a sorting facility only, and once the mail gets sorted it's taken to Dallas office for processing which adds to the delay. I know Fedex is a bit of drain on pocket, but what's the priority here..?
2. Attach all possible documentation
a. Cover letter with short paragraph on what are you applying and in what category (C-9) . Mark the mailing envelope with type of form as well (I-765 Renewal, I-485 based)
b. form + photo + fee (money order)
c. copy of I-485 receipt notice and I-140 approval
d. Copies of all previous I-765 approvals and receipt notices
e. Copy of FP code-3 biometric notice
f. copy of all H-1 documentation
g. copy of latest I-94
h. copy of Advance Parole, if you used it to enter it last time.
I. copy of passport (all pages)
Few stuff seems redundant, but I do it because all the supporting documents are for whatever you have specified in your I-765 application form. So, when officer is looking at your case and needs to verify the information in your application form and if the supporting documents are right there in front of him then it's just easy and quick for him to reach any conclusion on your case. Otherwise, he has to request documents from your main file (which contains all the documentation you must have sent to USICIS along with 485 or any other application) which takes time, and if the documents are not present in your main file as well, then he has to generate an RFE. And, the officer is not only looking at your file, he/she has hundereds of them in front of him...so any missing document puts you in back of the queue...
These are just my opinion from my experience and reading on various newsgroups and immigration websites. Please don't it as legal advice or something of that sort..
-jsn