While I appreciate that timed games are necessary when you're running a tournament, it is valuable to play a full seven every once in a while, especially to prepare for school ball where they typically play a full game.
This goes to marriard's point, that finding scrimmages against comparable teams should absolutely be a part of any travel team's itinerary. If you're just paying for an umpire and maybe field time, there's no rush to get through four innings. You can just play the game, and get everyone in, without worrying about the trophy hunt.
At 14u and 16u we would schedule 2 or 3 "friendlies" throughout the late spring and early summer. We would have 3 teams playing in a round robin fashion (Total of 3 games in which each team plays twice). These games were full 7 inning games. After game 2 we would make hamburgers and hot dogs on a grill for all 3 teams, and then play game 3 to finish the day. In many ways I enjoyed those days more than tournaments, although I did enjoy both in different ways.