Hi Quentin,
Interesting use case.
You could use The Events Calendar along with WooTickets to integrate with WooCommerce here. Essentially you would set up events spanning half-day intervals and set the ticket inventory to 1 (to prevent multiple customers from booking the same slot).
The only potential problem I can see is that you would have to manually create each “slot”, unfortunately at present their is no means of automating this built in to WooTickets.
Does that answer your question? Just let me know if you need any further information.