Custom product form or Checkout appointment scheduler

I am having a lot of trouble finding a solution for my website. I am creating a cake ordering system where I need to have people pick a specific date to pick up an order. I need to have limitations on how many cakes can be picked up in a day, as well as black out dates and a 48 hour window blacked out from time of ordering. I need it to be on a the custom product page, or the checkout page. Any help?

This is difficult. There may be options but many will be unsuitable.

You could add a date picker to the product form with restrictions on the available dates, but they would need to complete it for each product. If customers can purchase more than one product, it won't be suitable for you.

You cannot add a date picker or restrictions to the checkout page because it is completely locked down because of the sensitivity of payment information.

You cannot control how many products are picked up on one day either.