I've been unlucky in getting any Shiny from this event too so far. Same thing happened last year. I guess these Fossil Pokémon don't really like showing up Shiny for me.

I've asked the other friend with whom I can become best friends as well. Would 7 am your time work for According to google 7 am pacific time would be 4 pm my time. On this post it displayed you posted it at 5:02 pm my time. If 7 am your time works I'd likely open the gift around 5 minutes after the hour for a bit of extra time to put on your lucky egg if that's good.