Not quite 11 but we took two different family trips last year, one with my parents as well as my sister and her family and one with my wife's sister and her family, so the groups were a total of 9 and 8, respectively.
DW and I both get up early, get logged into our respective accounts, and sit across from each other. We are super nerds and planners, so we have a spreadsheet that has notes about which restaurants we want, preferred times, and the order of priority to try and get them. That way she is the lead on one reservation and I am on the other when we do these family trips. We only use online booking as waiting to get through by phone takes so long and we worry that more options will be taken by that point.
Between both trips we were there a total of 16 nights with a TS dinner every day and there was only one time when we did not have a reservation for everyone in the group within 15 minutes (ie one reservation at 5, another at 5:15). That was for Space 220 and that one was explicitly my mom's fault because she told us that she did not want to join us for that dinner because she had read it wasn't really worth it, so she said to leave herself and my dad off of the reservation and they would do something themselves. I don't know if she thought we just wouldn't be able to get the reservation or if she thought my sister's family or mine would change our minds, but when we were able to get the reservation then, suddenly, it became a huge ordeal to try and get my parents added because the FOMO kicked in hard. We were able to add one more person to one of the reservations before the trip and, at check-in, I spoke to the cast member at the desk and they were very graciously able to not only combine the two reservations so we could sit together, but make it work for us to add one more person.
So, in the end, what was one of the hardest reservations to get at the time even worked out for us. In fact, out of the combined total of 16 dinners, the only time that we were not able to combine reservations at check-in and all sit together was at BOG when we were there with my side of the family and it was 9 of us in total.
Bottom line, I would book online and I would try for two reservations of six in the OPs case within a reasonable amount of time of each other. This is almost always possible but sometimes you might have to take what you can get and then just keep searching for a cancellation at a slightly better time. There were instances where we started out with a 15-20 minute time difference but, by watching for new openings, we were able to bring several closer. Good luck.
