First, the hd650 doesn't need an $800 amp to sound good. It sounds damned impressive on a used lyr for $350...but so does the he400. Honestly the he400 and hd650 sound pretty dang good on a fiio e09k for $100. The jump from e09 to lyr was very appreciable but I also enjoyed the heck out of both hp's on the e09 and an odac.
The maddogs are a different story. They are geared more towards a flat response. For example, they do not color the bass but give it to you when the material calls for it. They are truly fine hp's and a steal at the price. They are what you might call a poor man's lcd2. Highly recommended.
Still, $400 is a big expenditure. And you definitely need a DAC and what does the lyr usually pair with? The Bifrost, which is another $349 which brings the price to $800 anyways.
I read all of the testimonies on this forum and I can't say that most people believe that the e09k is sufficient. I have heard people say that the HD 650 sounds very mediocre until you get that $400 quality amp and then the sound becomes much better. Although you say different, still.
Surely you have some sort of preference when it comes to the headphones listed in your signature? I would find it hard to believe that you listen to all of them equally.