Advanced order management

Hello,
We're using HikaShop Business to handle our food delivery service. Until now to handle time of delivery we used product features/variants, defining several features, one for each time of delivery. This system has been useful until we could deliver as many products as customers did order.
Actually we need to restrict or manage the maximum number of deliveries we can do during a time slice (let's say that we use to have 4 different times to deliver products). So we need a way to set up the maximum number of order we can deliver in such a time slice. If we use features/variants we can allow people choose the time for the delivery but we cannot set the number of possible deliveries in such time slice. Furthermore we cannot use the product quantity to set availability because we can sell contemporary 6 different products and we can't know before how many units of each products will be ordered. If we use availability in variants we have to decide before the quantity for each variant and this could be a strong limit for us because we can't decide the sold quantity of each product and we can't loose potential customers with a bad setting of availability.
So we thought that we should handle restrictions in the order management, but, actually we can't do it or we don't know how to do it.
Our needs are:
- we have 30 products in our catalog every week.
- we have 6 different products sold every day. Think to a menu in a restaurant.
- we need to manage deliveries in 4 time slices.
- customers can choose the time slice for the delivery
- we need to set how many products we can deliver for each time slot.
- when the selected time slot is full, customer can't choose it.

Is there a way to do it?
Should we continue using variants to allow people selecting the desired time slot?
Can we work on order to reach our goal?

Thank you in advance for your help.

Thank you very much Nicolas.

We're developing a custom plugin, as suggested. I've another question about this.

If we filter available time slots when they are displayed, it may occur that when an user is buying (but he/she hasn't complete the process yet), another user select the same time slot (available becaue the first user did not confirm the order yet). In this way that time slot could be overbooked.
Is there a way to prevent this?

Hi Nicolas,
thank you again for your answer and instructions.

Can we change the $do object in order to block the order and to display an alert to the user? We would like to display a message in which we explain why the order has been blocked. Is that possible? How to do it?

Thank you!