First off, welcome to Head-Fi! Sorry about your wallet....
As for your HE6se, First thing I would check and make sure that the drivers aren't stuck. It seems that even when brand new, both drivers can be stuck right out of the box. That will severely hamper performance (especially bass) but won't sound "bad", per se, at least not as obvious as like a blown driver. I made
this post a while ago on what to look for. It's pretty easy to check if you know what you are looking at.
Also, it might be helpful to know what headphones you are coming from. I know you said this was your first open-back, but there are a huge range of closed-backs out there that vary in price and performance. For instance, are you coming from a Skullcandy or a TH-900?
As for amps/DACs... the majority of this thread is discussing amps and it's hotly contested as to what is "required" to drive these, with everyone having a different answer. I would say before going down that amp rabbit hole you should make sure your set isn't defective and, if it's a sound signature that you care for. Everyone has different ears and an amp won't "fix" something you don't like.