CurseForge will not allow me to use both the base package and the alpha add-on in a modpack, since they are both included in the same project.

Please create a separate project for the Alpha Add-On. You don't even need to make it a standalone package, literally just upload the most recent version as a new project, and link to it in the original project.

I initially made this one project on CurseForge out of laziness since I really dislike making releases for CurseForge but you are right. They should be separate projects like they are on Modrinth. I will work on it. For now, try looking into editing the manifest in the CurseForge modpack and see if you can add a new line for the Alpha addon.