I would personally allow a corps to sign-up and just not have all of its units divided in three or four different coalitions. Same for regiments with several companies.
At the end of the day, it's still is a competition, which means that if you have worked hard on building several companies, you should be able to sign them up together. The independent regiment (be it light, line, art or cav) can look to form a coalition with other regiments they are familiar with, or sign-up as an independent structure and be matched with other independent structures.
Sure, regiments like the 33rd will start the competition with a significant advantage due to a natural synergy between their different companies, but they can still be beaten by individual regiments teaming up together, as it was proven in the past.