I messaged the campaign developer. Adding the weapon entities in the mission text file should allow the custom weapons to appear in their designated locations in the game. The developer confirmed it will be added in the next update, although it may be some time before that happens because this is a minor bug. It makes more sense for him to fix several smaller issues in each update, not just one.
Is there anything low effort that could be done on the server via a script or otherwise to make these four weapons appear in the meantime? If we could test this change to ensure that modifying the mission text file will allow the weapons to appear, I could also confirm with the developer this change will fix the issue.
If making these changes will be too much effort for now, then that is okay and we can keep the campaign as is. We don't need a custom alServ version of this campaign like we have for Lost. This isn't worth spending much time on when it will be addressed in the future, but we don't know when or if the developer will release the next update.