Hellokit, here’s An Interesting(dumb?)Thought. Is It Ever Possible In These Tight Component Installations …
… to dissamble or partially dassamble the component (in this case an alternator/pulley) and take it out in pieces or subassemblies and then reverse the process for installation? It sounds like in this case, there just flat-out wasn’t room to get anything out of there larger than an 8mm nut. Also, maybe there wasn’t even enough access to work on the alternator, like maybe you had trouble even seeing it.
Have you worked on a “ship-in-a-bottle” ?