I would start by trying for one reservation for your entire group because then the table assigner knows you are a group of 12. If you try for multiple reservations for smaller parties you could easily be seated at separate tables. Seating assignments for HDDR are made several days in advance so you would not be able to show up and ask to be seated together.
It is not necessarily that the computer system likes even numbers of four, but rather the system prefers even numbers (2, 4, 6...) rather than odd because most tables have an even number of seats and the system wants to fill all the seats at the table. When booking reservations at any Table Service restaurant if you book 3 separate tables of 4 each the hosts/hostesses at the restaurants will assume 3 separate parties and it will be less likely you will be seated at one large table. If you don't mind being split up, then there are more 4 tops in a restaurant compared to a table for 12 so finding reservations for parties of 4 will be easier.
