On the flip side of OP's question. I typically travel with 7-9 in our family, travel peak seasons (Christmas week, 4th July, Spring Break, etc.) and start booking at 04:00 at 180 days out and have never been able to directly book a table for my party size. After some pretty intense frustration two years ago, I learned how to play the system (with the help of Disney CM's). What I do now, is book a table for 4 (I can always book that size table within 15 minutes of my desired time). After I have all my reservations for the day, I call Disney Dining (once they are open for the day), explain my predicament and they will book a second table at the same time (the automated system will not let you do this under the same name). Sometimes the second table can only be booked at 15 minutes later.
Now that I have multiple tables of 4 or two 4's and a 2, all within 15 minutes, I have been pretty lucking in getting the restaurant to pull the tables together or seat my party in separate tables that are adjacent. I have been lucky in stopping by the reception desk of the restaurant earlier in the day and describing my plight and I show up with the full party at the first reservation time and end up getting us all seated together. Not ideal, but workable.
Now, contrasting this planning system to our family's current trip to
Disneyland this August.... I stuck with on-line booking as soon as the 60 day window opened up (60 day planning is much more stable than 180 days with my group) and was able to book every dinner and dinner/show package for our party of 7 directly. No calling CM's or maneuvering separate tables together. Much nicer. I do not believe that there is unfair treatment but the system really is set for table sizes of 4 and there is no logic in the system to make trade-offs or extrapolations. Fortunately the CM's can make some changes for you.