Way below your price range ($350 US), but pretty much exactly the signature you describe, are the Audio-Technica ATH-R70x, which someone also mentioned above.
They are open-backed headphones, light and ultra-comfortable, fairly flat with a slight bass boost, not sibilant, very outside-your-head soundstage. They do best with an amp. The specs have a frequency response of 5 Hz to 40 kHz, so if you want to pump up some extra bass those low frequencies are fully available.
Nothing bangs you over the head from these, in any range, and they won't blow you away instantly with boom and sizzle. But then, when you listen, every note is clear.
They do have an ultra-long cord, 9 feet.
There are a lot of reviews on Head-fi and elsewhere, to be taken with the usual YMMV.
https://www.head-fi.org/threads/audio-technica-ath-r70x-in-depth-review-impressions.765004/
(I am baffled at ones that don't hear an expansive soundstage. Try them with an amp, or for that matter try your own PM-3, on the Les Siecles recording of the Saint-Saens 3d symphony, fourth movement. Organ, orchestra, all going full-tilt, and you can hear where every violin or trumpet is.)
Meanwhile, the ever-cranky Crinacle gives them an A- on his site, up among the mostly four-figure 'phones.
Since Audio-Technica stuff is widely distributed, you can probably find them with a good return policy at Amazon or at pro-sound online stores (Canada must have the equivalent of US stores like B&H or Sweetwater), because they are aimed at recording-studio engineers. So you should be able to try them out too. I had listened to other AT models (the M series) and was completely unimpressed, but these are a whole different approach.
Mainly neutral, a touch of bass emphasis. One thing I don't like is silibance in the treble. Clear treble, but no painful areas.
I do like my PM3s a lot, with EQ applied similar to the Harman curve, some decrease to decrease bloating in mid bass.
I do like to up the bass on some music, such as rap and electronic, so it is important that I can EQ for this without distortion