Not a bad concept, but I'm really not sure how this fits with the jam theme. It didn't really take away any standard platforming mechanics. There's also nothing about it that's actually hack-and-slash.
The controls seemed a bit unnecessarily awkward. There's no advantage to not having a sword equipped, so I think it would have worked better to immediately equip the next available sword after running out of a type, automatically equip a new one if you pick it up without another sword readied, and just use two buttons for cycling between them. Holding down middle mouse is also a decidedly weird way to use an ability, and I think holding shift or S (down) would have been more intuitive and comfortable.
That all said, I do definitely like the idea of each sword having unique, often unexpected abilities, and I'm sure there are interesting ways to expand this idea.