Ok, so here are my findings (TLDR: I had what I needed all of the time with the Boss Katana: Go). The Boss Katana:Go does have a Pitch Shifter effect. It does the job, but has issues. As is the case with many multieffects that try to imitate a Digitech Drop or Boss XS-1 Polyshifter, it has artifacts, even at just 1 semitone. You can hear a warble when a note or chord are held. But the good news is that it also has an effect called Peddle Bend. This has been recommended for years by owners of Katana amps as the best way to drop down a half-step (I’m not sure how far down you can go before it sounds like crap as I was only looking for a half-step). So I can achieve the drop, but I waste the Peddle FX (Wah) slot in the chain. I personally don’t know of a song in Eb that uses any kind of Wah, so that isn’t a loss for me. I tried to do the drop with the Fender Mustang Micro Plus, the ToneX Plug, and the Positive Grid Spark Neo, but none of them have an effect to pull it off. I also tried a Blackstar Beam Solo at a guitar shop today and it didn’t have a compatible effect to tune down. The only other popular headphone amp out there that I am familiar with, the NUX MP3 Mighty Plug Pro, according to all documentation I found, doesn’t appear to be able to do it either. But I didn’t verify that myself. So, if you want a headphone amp that can drop down to Eb, so far the best I can recommend is the Boss Katana: Go.