Well it depends. I had to take some drastic measures myself due to constant rain and high humidity, freeze/thaw... ugh.
Does it really reek of ammonia? It doesn't sound like it from your post, so you're still ok. For the most part, the high humidity levels alone won't ruin it for you. You'll want to make sure you're getting enough ventilation to help the air change. How deep is your litter? And more importantly, how much of your litter is composed of droppings?
I've curbed problems with high humidity by using DE (occasionally), adding shavings, deep stirring, adding dead leaves (helps fluff up the bedding), and even partial bedding changes if ammonia becomes a problem. You should be fine by what you're doing now. Just monitor your ammonia
I have a raised 5x4 coup with 12" bedding and found my bedding had a high poop ratio to shavings. With the cold, rainy, freezing, humid weather, I found that the bedding was starting to compost on it's own. If I had a bigger coup, I would be happy about it, but this is not good news for me. It's composting (hot) since there's enough moisture in the bedding to start it. After much investigating (no signs of water leaks), I came to the conclusion that the BOTTOM/FLOOR of my coop was creating condensate due to the temperature difference between the freezing outside and the warm inside of the bedding. The floor is a 1" subfloor, with vinyl, and it didn't occur to me to add a moisture blocker of some kind, since I figured the bedding would be enough of an insulator. I never said I was a builder, lol.
So if dig all the way through the composting bedding, there's a thin layer of wet bedding on the surface of the vinyl. Ugh! I had to change out 5, 5 gallon bucket fulls of bedding and stir up with DE to take it back to acceptable levels.