I have spent a lot more time playing with this and I'm still not much further than I was. UCSD seems to have no concept of User/Group membership from AD, it only knows about the actual names of the groups. I'm really hoping I am wrong on this point because if I'm right, then integrating AD groups into UCSD really servers no purpose other than to save you the hassle of creating a bunch of groups, which really isn't saying much.
I've attempted to progress with the multiple user access profiles route, but I am hitting some stumbling points there as well. If I understand this correctly, the primary group that the user is assigned to in UCSD must also be assigned a group share policy which includes the additional groups that you would like the user to be able to manage. Only then will the additional groups be visible in the user profile management section or the user. However, just by doing so, a user will by default see all of the groups listed in the group share when their primary group is changed, until you go in and uncheck the box that says "show resources from all groups that the user has access" in the default access profile entry. Once you do that though, you need to add individual entries for each group you want them to have access to, and then the user will be responsible for switching between profiles in the UI.
Can anyone confirm that this is indeed the way UCSD works, and that there is no better way to accomplish what I am trying to do? Again, I really hope I am wrong and there is...