I think what you’d need to do (without changes to core) is create a new group, clinical-members that is the actual group, then move all the members to that group and out of the existing one (and if those users get permissions from that group, you’ll need to adjust category permissions accordingly). Next, create a clinical-announcements user with the group email address as its address, and add it to the clinical group. Then when people mention @clinical it’ll go to the single "user?
Wait. You don’t need a new group. After renaming the group, make a new user with the original name of the group with the shared mailbox as its email address.