I used to run 8-team tournaments in two worlds. One was 'King of the Bluegrass' and hosted by Kentucky St. The other was 'Silver Stake Invitational' hosted by Transylvania. The first two rounds were played in exhibition with the winners meeting on the 2nd day and the losers playing likewise. This gives you two bracket winners. .
Then, in regular season play, you faced each of the 4 teams in the opposite bracket. Whenever the two bracket winners meet, that's the championship game. The other placements are based on the overall tournament record.
You just have to stress to the coaches: Do NOT schedule your 2nd exhibition game. We need it for the 2nd round of the tournament