Heya,
Yea, they're expensive, they're the upper tier of the PRO series line by Ultrasone. They're $330 from Amazon. That's within your $400 budget. Leaves room for a Fiio E11. So for $400 you have pretty much the bassiest of bassy headphones, durable, detachable cord, carry hard case, and a sleek design that puts plastic neck jewelry to shame.
Very best,