I know your pain on finding some crinkle finish black plastic that matches or complements a vehicle interior. In a previous job, I installed equipment into vessels and high end vehicles for emergency communications. These were used by VIP's and politicians around the world, they had to look nice.
I never used a battery box for the plastic, but it does make good sense. Battery boxes work well because they are made to withstand the temperatures found under the hood. They are made to contain acid from the battery for a short time if they leak, and do this while protecting the battery and looking nice.
I had to go to specialty plastic dealers to get sheets of high density black plastic. 4x8 foot sheets, and then cut it down like plywood. Very expensive, looks nice, but the same material as the battery box. Unless you have a couple dozen vehicles to do installs on, it is not economical. Auction sites sometimes have remnants though for those that may need it down the road.
Good job on the install. Looks nice and is probably very functional.