The HD650's don't have the sound attributes you want so sell them and get some headphones that are better in those areas.
Using an amp to compensate for faults in the headphones presentation is never a good idea because the amp is likely only going to be good with another headphone that sounds similar to the HD650's.
Also don't believe the hype that the HD650's scale well either. Every headphone in existance will improve with better source/amplification it is not just the domain of the HD650's. I had a pair and I tried various amps including my current Woo6se and silver & copper aftermarket cables but they never improved THAT much. The only thing I did not do is try them balanced because I had already decided to sell them by the time I got my balanced amp.
My recomendation is to buy a s/h LCD-2, plenty around at the moment, they are not difficult to drive and get a better amp when you can afford it.
Don't build your system around its weakest link