I cannot for the life of me defeat what I need to (vulpactias), but I also can't get any new lorwolves from exploring to help me with it until after I've finished it, it looks like. Do I just explore in other areas to get new lorwolves? And if not, is there a way to get stronger more easily then just campaigning in an area where I can defeat the locals?

There is a "Wild Wolf" encounter that gives you a chance (albeit a low chance roughly around 10% or so - this is user data driven and not 100% accurate.) to successfully befriend a wolf. These encounters don't appear in the first area of each pack territory, but will appear in the areas that look like swords. You can check what areas will give you the encounter by clicking on one, and scrolling to the bottom of the page. It should show you what scenarios you can encounter in that area. Here's a Wild Wolf befriending guide - Click!

If you have the pebbles, you can also purchase new wolves from the Flea Market to help aid you in Explore.

Last but not least, I run a free wolf giveaway if you're interested! - Boop

Also, if you have any companions, you should put them on your wolf or wolves that you are exploring with. That way, you can add them to your explore party and they will help you defeat things. c: