You can just email it in and say "in reference to renewal for (license number) please find the attached proof of gun club membership"
I did that, got a confirmation email saying they forwarded along the info to the appropriate person. I think it even gets the process going faster. I checked a few days later online and it was already approved (less than 1 week from submitting online to approval) I suspect when they open up your rifle to link up the membership, they just smash the old "approve" button while they're at it