Is there any way to become Firearm Instructor qualified in the Navy Reserve, and if so, how would I go about searching for that opportunity?

I would talk with your chain of command and local leadership. You may be trying to reinvent the wheel here. I'm sure this wouldn't be the first time your unit has qual'd or sent someone up a a third party location/unit to qual or be certified for the course. If your leadership if unaware talk to the training section. It is literally their wheelhouse for such things.

Good afternoon PO3 (Join to see). Excellent post. Thanks for sharing this Shipmate. I believe for Navy Reserves you can talk to your work center supervisor or LPO, or training PO to see if there are any courses that you can sign up for and either put on TAD or TDY orders depending on available funding.