Is it possible for non-essential USMC personnel to get their jump wings?

Several years ago it was. The USMC gets "class seats" at the Division Level which they farm down to Regiments/BNs. We don't use all of them. Most of the time they will go to some "hard charger" as a reward/incentive. The trick is talking to your local training NCO (inside Ops S3) and finding out if there are any class seats and how you go about getting one.

On a Reserve side, I'm not even sure how you would go about it since they would be Active Duty orders for Training, which is unit/training funds making it more challenging.

Back in my day it was All about RECON. But I was awarded my Silver Star and the one star that gave it to me noticed I was going to Marine Barracks at Rota. He said the most Beautiful thing on a set of "Class A's " is wings and asked if I would be interested in going to jump school. Sure! I'm home on leave get my orders and bingo, made my quals at Benning and my additions with the Spanish in Spain with some Green Beret that trained Spanish forces.

Had my slot to jump school "stolen" by the Bn XO. The Bn SgtMaj explained that I served a useful purpose, whereas the XO was just breathing our oxygen. The SgtMaj assured me that if the Marine Corps needed me to jump from an airplane, there was plenty of time for training on the flight to the drop zone.