That's one of the few trips where I'd bring two pairs of shoes – both low cut trail runners or maybe one of them beater running shoes for the river portion ( plus wool or synthetic socks.) then change out of the wet ones after the narrows and tie them outside your pack. An old broom or mop handle is longer, tougher and therefore better in the river than a trekking pole. Add your own strap to it.
I was last there in March with my 9-year-old daughter, so the water was pretty cold. Most people had rented dry suits, water shoes and big, thick wooden poles. And we walked by, with none of that, holding hands where it got fast or deep.


(There are deeper, faster spots than these photos, but I only took my phone out of its dry box in the calm spots).
For sleeping in June, I'd bring a light quilt and tarp. The tarp to minimize night-time condensation if the nights are clear and windless.