A different headphone will give you the most dramatic change for sure. Whether you will like the changes or not is a different story.
A good tube amp always helps the HD650,but its not going to be a night/day difference.
The HD650 is a warm headphone with a pretty slow response,so depending upon which genre of metal youre into that can make faster metal sound muddy/blurred.
For hip/hop you want something with big/deep bass. The HD650 has nice midbass for thump,but doesnt dig too deep into the sub-bass region.
For jazz you want those mids to be good,which the HD650 has.
For classical you want an expansive sound stage,something the HD650s do not have.
As you can see its not an easy answer. Do you buy 2-3 new headphones,one for each genre? Do you buy one new pair and try to get an all-arounder type headphone?
A good planar might be your answer. As to which one im the wrong guy to ask. Many people will say a HiFiMan headphone. Many people,myself included have had horrible experiences with their build quality and not exactly state of the industry customer service.
The Audeze LCD-2 is in your price range,but sounds similar to what you already have.
I probably confused you more than helped,but its not as simple as throwing gobs of money at an issue and getting the results youre looking for. If you can narrow down areas of the sound where you want improvement that will help quite a bit.