Nice place!
Colin, don't judge all K340s on that particular pair. That pair is the polar opposite of my old pair. I had them with me for a couple of weeks, as Alex sent them to me after he recabled them. I made the wooden trim pieces for a different Matt, who owned them at the time.
I also found these to be muddy, with an odd midrange coloration. I assumed these were what people refer to as the bass heavy version, but they sound nothing at all like the pair I owned for 27 years, and I did plenty of direct comparisons.
As for the K1000, toe out can definitely help to tune them to your taste, although I tend to like the treble. I also am quite fond of using them with an active subwoofer. It's an experience that's hard to explain. Much closer to speaker presentation than any headphone can come. I'm still kicking myself for not buying them back when they were first introduced. They are my ultimate headphone.