Take a look at the Combat Phase rules on p.14:
Sometimes more than one model from each side will become involved in a single combat. In this case, the models should be separated into a logical number of single combats, depending on the sequence in which they joined the combat and which models are in base-to-base contact with which. Common sense needs to be applied in these situations, and the golden rule is that only ONE side will ever have multiple combatants in any given combat.
That should cover your query about how to run through large melees.
As to games ending up as a big scrum in the centre... while the focus of the period (and the game) is on hand-to-hand combat, there are plenty of options for a different approach. As William said, vary your tactics - just because you're going to end up in melee doesn't mean that they always play out the same way. You could also change your troop options - while ranged weaponry is limited to a degree, consider increasing the number of teppo or yumi in your Buntai. Also, consider running through some different scenarios, or even creating your own - perhaps one in which a Buntai is forced to divide its forces, or one where one Buntai must evade the other (this works well for a Bandit Buntai attempting to escape from a superior punitive force). You could also use the terrain to mix up the possibilities - a tight urban set-up would reduce the mass scrum effect by introducing a number of routes through the board, and limiting the number of figures that could contact each other at any one time. Throw in routes across rooftops and the aforementioned yumi and teppo become really useful!