As someone who has recently gone from not being into headphones at all, into becoming a veritable headphoneaphile

I think I may be able to offer some advice here.
First of all, the Sennheiser headphones you have are some of the easier to drive phones they make, that is, they will be driven pretty well out of the headphone jack of your integrated amp, and the improvement may perhaps not be as great as you want for getting an amp.
Having said that, they could still improve noticably with a headphone amp I guess (not having heard the 590's).
Recently, I got some Beyerdynamic DT931 headphones. They sounded alright out of the headphone jack of my Rotel amplifier, but there was definetly room for improvement, the sound was overtiring and hard.
I recently got a Meier Audio Corda HA-1 headphone amplifier, a supposedly synergestic mix for those particular headphones. The sound is dramatically improved in dynamics, refinement, smoothness, it can also go louder and has more impressive bass. It also has a nifty crossfeed feature, which sends musical information from the left channel to the right channel, with a slight delay and vice versa, and this gives more of an impression of using speakers (its not perfect, but it goes a long way to reducing fatigue when using headphones).
During my research, it has been suggested that the minimum of a Corda HA-1 or META 42 (a DIY amp) is recommended to see a useful improvement on the headphone jack of an integrated, and judging by the performance of the Corda, I'd say it was true.
So, I'd say go for it, if you intend to spend a lot of time listening to cans. Just one thing though - I have found that headphones can never quite match the impact and slam that speakers can have, although you can get bassier headphones, its pretty much impossible to recreate the feeling of bass you get from speakers.