I quite like the 2nd option to be honest, as you don't need to keep reloading ammo all the time (or at least as often), with the one exception in that it takes up more of your valuable inventory space.
Wasn't there mention of a quiver at some point in the past? If this isn't completely out of scope for development now, maybe this could be an additional place to store ammunition only, whilst still maintaining the reference to the smart stack?
Depending on how they plan to implement the PS4 version, I think this could be quite difficult to use (especially, if there is no visual cursor, but just a highlight on each slot as you navigate around your inventory). sorry, but I also don't think this will be particularly intuitive either.
I'm wondering if an additional option would be to still have the right click menu, but doing so shows 1-4 additional slide out ammunition slots on the weapon so you could assign ammunition into it. Maybe tie that into weapon tier or progression as well, so better slingbows have more ammunition slots, making it so you don't have to reload as often.