This is a classic strategic dilemma. Your objective is not only to seize the opponents territory, but to destroy or neutralise his armies. By pushing him into a corner, you allow him to concentrate his force.

One technique is to try and lure the AI out of the corner by leaving a weakened besieging force in province 3 or 4. If you switch your main army between bordering provinces, you can sometimes fool the AI into attacking your main army (or a substantial force at any rate). In a defensive battle you should be able to inflict heavy losses on the enemy.

Attacking a mega-stack is more of a challenge, but not impossible. Sometimes you will need to send in troops who can inflict damage without winning battles, e.g. horse archers, and allow the AI a pyrrhic victory or two. Use a crap commander who won't mind getting the "good runner" vice.