So it turns out that if I add the Handler Mappings on the Website and Application level, everything works beautifully. I was only adding them on the server level, thus IIS did not know to map the asp pages to the IsapiModule.
So to resolve this issue, go to the website you want to add your application to, then double click on Handler Mappings. Click "Add Script Map" and enter in the following information:
RequestPath: *.asp
Executable: C:\Windows\System32\inetsrv\asp.dll
Name: Classic ASP (this can be anything you want it to be