Your other choice is to buy dog crate covers not just for soundproofing, but also for the dog’s privacy and security.
The best dog crate covers are those that convert the crate into a cozy atmosphere for the dog. This would prevent them from being anxious and would help them stop barking.
For convenience, select the covers which are strong and washable. You will have to regularly wash the cover as the smell of the dog would stick in it.
Consider the material being used, too. Make sure they’re skin-friendly, soft, hygienic, and dirt-repellent, if possible. Most are made with a premium microfiber fabric structure.