With the help of support, I was able to find a bug report that outlined the problem. The workaround is half-baked and needs a rewrite. Does not seem to be a root cause identified yet.
The README file in the deployments folder was the key to figuring this out, since I have next to zero knowledge of JBoss.
In the deployments JBoss root folder, you may see some files that end in either .undeployed or .failed, which are most likely the root cause of why you're getting these 404 errors. For me, the problem was these files:
Inside of each of the download.war, log.war, and log-download.war folders, I confirmed there was an error and WEB-INF folder. If you don't have those in there, copy them from somewhere like help.war.
Remove the .undeployed files, and replace them with empty .dodeploy files:
This should trigger JBOSS to read these files and then deploy these folders. After a couple seconds, these .dodeploy files should disappear, and you should see new files in the deployments folder with .deployed suffices, which means you should be good to go and your 404 errors should be gone. Worked for me!