@epicurean
First, congrats on getting through NG+, I was one boss away from doing it, but you all know what happened T.T
Also, you can get Ronin's Ring on 4-2 on the slugs nest. In the middle part of the nest, there is a tunnel to the right side of the screen, in there you'll find an 4 slug ambush and a corpse with the Ring and the Gripless Katana there.
Current PC Build
CPU - i7 8700K 3.7 GHz (4.7 GHz turbo) 6 cores OC'd to 5.2 GHz with Watercooling (Hydro Series H110i) | MB - Gigabyte Z370 HD3P ATX | Gigabyte GTX 1080ti Gaming OC BLACK 11G (1657 MHz Boost Core / 11010 MHz Memory) | RAM - Corsair DIMM 32GB DDR4, 2400 MHz | PSU - Corsair CX650M (80+ Bronze) 650W | Audio - Asus Essence STX II 7.1 | Monitor - Samsung U28E590D 4K UHD, Freesync, 1 ms, 60 Hz, 28"