Help figuring out how to handle TV appearance and Amazon availability issues

We have a major national TV appearance with our product in a few weeks, but it’ll take 60 days to get the product from our manufacturer. (We’re currently sold out on Amazon FBA)

Our plan was to switch from fba to manufacturer fulfilled and tell customers the estimated deliver date is 45 days.

I just learned that the max handling time via Amazon is 45 days.

Does anyone have any ideas for how we can manage this?

Thanks for the help