Depends on what you mean by involved. You have to give them an address to send the confirmation of resignation. They will send the resignation to the local bishop for processing. He may or may not contact you, and may or may not expedite your resignation.
None of that matters. Your resignation was effective when they received it. How long it takes them to finish the paperwork is irrelevant. They will get it done in about 60 days or less, sometimes much less.
You could give them an out of state friend's address to sent the final letter to. You could give them your cell phone number. That area code can be from any state. People rarely change cell numbers anymore when they move.
Btw, to the people who refuse to give the bishop a cell phone number, you have just made it so the only way the bishop can talk to you is to show up at your mailing address in person. Is that really what you wanted?
Keep it simple. Send in your resignation. If the local bishop calls, tell him you've resigned, and to send in the paperwork ASAP. Don't add a pointless game of cat and mouse to the proceeding. It's a waste of your time and energy.
Be prepared to provide some other identifying information besides your name. You can't use your address (they haven't matched it to you yet), and they'll need some other bit of info such as your membership number, birthdate, or membership record number to know whose name to drop.
I asked that the bishop not contact us, and he didn't.
Provide your name and some other bit of info in the database, and you should be okay.
Send in the "ticket to freedom and happiness" via email or post mail. You will eventually get a reply. They will contact you confirming you are out, by letter, and maybe a call if they can reach you. The (new) bishop must have gotten my number from a local sourch or family member, probably. He called and I said yes I am me and no I haven't changed my mind. That was it. A few weeks later the letter arrived.