Finding a headphone that ticks all those boxes is tough! DJ headphones tend to prioritize high isolation and a darker sound curve, both things you might not always want in a music headphone. The isolation usually comes from higher clamping force, and the darker sound is so that you can monitor bass at higher levels without destroying your ears with treble.
I’d probably go for two headphones honestly, in your particular scenario. One for DJing and one for music. If you insist on trying to cover all the bases…the best model I can think of that I’ve tried is the Beyerdynamic Custom One Pro. Its adjustable sound signature means you can tweak it to be more in line with DJ pairs, its ear pads are super comfy and isolating, and its replaceable parts mean that it’s easier to repair than other models.
Otherwise…have you ever used a Sennheiser HD 25? You can get them for around $140 or so, and they’re trusted in the DJ profession for a reason. I know many that swear by them. They aren’t the most comfy things in the world…if you really want to go all in, the Sennheiser HD-26 is basically a more-comfy version of them. But it costs more than double the price.
After the $140 for the HD25, I’d spend another $99 or so on a nice consumer-focused pair, maybe even a cushy gaming headset. Gaming headsets get a lot of flack, but many of them are designed principally around long-wearing comfort and solid sound quality, so I don’t really understand the hate. The Arctis 3 2019, HyperX Cloud, Kraken Tournament Edition, and Elite Atlas are all absurdly comfy models that won’t bust through that $99 price point.
Those are just my thoughts off the top of my head. Hope that helps you out! Thanks for reading.