@Lex Sheer numbers can work against a fixed number of targets. The problem is these overflowing dungeons are presumably expelling unlimited opponents, so it's likely Fuuga has unlimited troops at his disposal. Not sure how they're going to resolve that, turning off the dungeon making program would only stop new dungeons from forming, it won't do anything against the existing ones which is what's presumably driven out the northern species.
If they can shut down creating new dungeons then the existing ones are just going to keep producing more monsters at whatever rate they were before. The total population will probably stay the same since there are only so many that can live on that amount of territory, probably just a lot of turnover.
Not to say it'll be easy, it would be a massive military commitment to send an expedition up there even if they can get another portal working. But once they can start shutting down dungeons and thinning out the swarm by reducing numbers and replacement rates it will get easier as time goes on.