If you are stuck with "anytime dining" on "personal choice dining" ship, there is one other option. If you find congenial tablemates on the first night or two, you can ask as a group for a standing reservation for that table for the duration of the cruise. With such an arrangement, they usually will tell you to just go directly to your table at the appointed time. From then on, you have functoinally the same arrangement as "traditional dining" but in a different dining room.
If that does not work out, there usually are a few people who don't see eye to eye with their tablemates on the first evening or two of the cruies and ask to switch. If you see the Maitre D' on the second day, he probably will be able to move you to "traditional dining" at either seating.