The main reason the Denon's "need an amp" is in my opinion the impedance issues. Too many products have too high of an output impedance to pair well with them. Because of that, I don't think the E9 is a great pair with the D2000s.
As for an updgrade from the E9, I guess it depends what you're looking for and what budget you have.
The D2000 and HD-650 are fairly similar in sound signature but present pretty different draws to an amp, so you might want to decide which one you prefer and focus on an amp to pair with it. It might be time to start considering
What about source? Were you using the E9's DAC? If so, the best thing to do is probably upgrade source.