I looked up those phones and they seem to be more of what I would consider a "convenience model" rather than an out and out home listening, hi-fi type of headphone. I think that you might find the difference between what you have and something made more for home listening pretty dramatic. Of the two the I have, I would recommend the HiFiMan Sundara, which I got used for $200, though they seem to go on sale new for not much more than that. They're really detailed and open sounding, at least compared with the Sennheiser HD6xx (which are a bit cheaper), with the Sennheisers being a bit warmer/smoother sounding, which can be nice as well.
One thing to consider is your amp. I might ask around here about the headphone output of that amp, particularly if you go for a headphone like the Sundara (or pretty much any with the same kind of planar magnetic driver design) as these things take a lot of juice and not every built-in headphone output is going to be adequate to make these things really come alive. I bought a pretty nice, more than powerful enough headphone amp, A Gustard h10, which again, I was able to find used for cheap, though I have to admit that with my vintage amp, a Marantz 2270 receiver, the headphone out on it is good enough that the improvement with the dedicated headphone amp isn't dramatic. It's the kind of difference, or lack thereof, which unfortunately isn't really apparent until you're able to get the thing home and compare.
I'm lucky that I don't have neighbors that are bothered by my music (it helps that the side of my house with the listening room is separated by the width of two driveways), but even though I have the luxury of being able to play my music fairly loud at about any time, sometimes I like to do a headphone session. I find that I get different things from the music with the headphones...