It's 100 shells that I can't use unless I stop to manually reload. How is that in any way sensible?
You can still unload a shell box into your inventory: while this will take up an extra inventory slot, it'll let you use Shottyman all the same. Whenever your inventory shells run dry, just unload another shell box. As a matter of inventory management it should only be of minimal concern.
To be honest, you'd think the way Shottyman works would ONLY allow using shells from ammo you're carrying in your prepared slot. It's hard to believe that the player can constantly reach into his backpack to reload while moving and would make far more sense if he could do it with a box of shells in, say, his belt or pocket (I have no idea "where" the prepared slot puts stuff, but it is a faster action). Perhaps shell boxes could grant auto-Shottyman instead? (This is also a question of balance, however, so there would be other necessary changes if this were to happen.)