NJ starts the team tournaments a three weeks before the weight class state tournament. The state is divided into 4 sections, 4-6 teams in each section. There are 4 public school divisions(we call then Groups) based on student population and 2 prep school groups In one week 4-6 teams in each section duke it out for the division championship of the group. the 4-6 teams selected for each section are picked from a computer power rating. The 4 section champs meet the following weekend to determine the division champs. Teams that do not make it into the team tournament usually arrange duals among each other to remain active.
The following week we start the individual championship and a award a team title for the area. Here teams of all sizes meet to determine a local champ. Top three placers move on to the region tournament, where the top three placers move on to the state championship in Atlantic City. Everyone except losers in the first bout of the district tournament all allowed one loss before being bounced.
If you run your individual tournament before the team tournament, you will have a lot of wrestlers that are competitively idle for 2-3 weeks getting bounced out early. I see that impairing the team strength for the dual title. Conversely teams can remain competitive wrestling duals while they await for the team tournament to finish.