Wow, big gap, I wonder why it was done like that. I suggest the backer rod then fill the shower full of water with the drain covered to weigh it down. Then use 100% neutral curing silicone. If it's just white GE makes one that is guaranteed to not mold. I have used it and it's very good. I believe it's call Supreme. Just make sure you us a Neutral curing silicone. You can get it color matched through Mapei, Laticrete etc.

Most big box stores will carry it. Do not use caulk or Siliconized caulk. On all change of planes you must use 100% silicone. Caulk is just gonna crack. Use a smoothing tool to put the silicone in and a spray bottle with water and a couple of drops of Dawn. It will give you professional results. Once put on give it a long time to cure as that is one huge gap. Then drain the water and you should be good to go.