I have a brass shower drain that is leaking causing damage below (of course).

I unscrewed the inner ring of this flange design and removed the neoprene (I think) gasket which certainly appears to be very worn and shows signs that it was likely the culprit. My question is, do I try and find another one as a replacement or am I better off just using plumbers putty to fill the void? Or maybe silicone?

Don't try to fill the gap with plumbers putty. If the old ring degraded due to age or chemicals look for a high quality replacement. The drained worked when it was installed so just bring back the newness with a new seal, most are neopreme.

If I were you I would get another gasket

LTH51

OK. I'll hit a plumbing supply shop and try to find a replacement gasket.

My access is limited to top side only on this project. I am a bit concerned that perhaps the leak may be on the outside of the brass drain, that is, between the fiberglass shower floor and the drain. I have no way to fully remove this due to top access. Will a bead of silicone do anything the stop an outside leak? The floor of the shower does seem to have a small amount if give or flex in spots.

I have a brass shower drain that is leaking causing damage below (of course).

I unscrewed the inner ring of this flange design and removed the neoprene (I think) gasket which certainly appears to be very worn and shows signs that it was likely the culprit. My question is, do I try and find another one as a replacement or am I better off just using plumbers putty to fill the void? Or maybe silicone?

If you have the neoprene gasket under the drain lip then it's installed wrong.
The installation goes like this,(see image). First a small rope of plumbers putty or silicon jel is placed on the drain lip and the drain inserted in the base. Now below that the neoprene gasket, then the fiber anti-friction washer and finally the nut that secures the drain assembly. You will have to open up the ceiling and re do the drain. While you have it open it would be a very good idea to prop up those "spongy" spots with mortar, cement or blocks. Good luck, Tom

I have a brass shower drain that is leaking causing damage below (of course).

I unscrewed the inner ring of this flange design and removed the neoprene (I think) gasket which certainly appears to be very worn and shows signs that it was likely the culprit. My question is, do I try and find another one as a replacement or am I better off just using plumbers putty to fill the void? Or maybe silicone?
You could proberly do either but I would re place the gasget with a new one there probely not that expensive