First off, hi, merry Christmas for those who celebrate it!
So basically, Molly told me he wanted to move on Toy Day, but he wouldn't ping me because obviously it was a freaking festival. He won't ping me today either. Is there any way I can stop him?
Try the wet suit trick? It'll generate a ping, and if Fang's outside his ping might be about his moving.
Also, when did Molly tell you that he wanted to move? If it's today or yesterday, try waiting until tomorrow if the wet suit trick isn't working. Sometimes a villager won't ping you they're moving immediately when the rumour starts circulating, and they'll ping you a day later.
I've never had a villager not ping after I'd been told by another that they were moving - unless it was a villager I hadn't spoken to in a long time. I assume this is not the case for you.
Just keep trying - walk in front of him a lot to give him the chance to ping. If he doesn't, then save, quit and go back in and try again. If you have a secondary character in your town, try going into the game with that character and talking to Fang; then go back with your mayor and try walking by him again. That tactic has worked for me before with a villager who seemed not to want to ping.