Owning HM-601 it is rather warm sounding, the highs are rolled off, and the Grado's are known to be slightly bright sounding headphone. So what you're doing is actually the right thing, pairing a warmer source with a brighter headphone usually balances out well. It shouldn't dull them to much just enough to tone them down. Basically, what you want to do is marry the two tonalitys together (player/headphone) which creates a sibbling of the two. (think of it like a balancing act). It's hard to say just how much HM-601 will tone them down usually the headphones signature pushes through slightly more depending how transparent it is. I think what you're wanting to do has the recipe for a good paring.
Edited by H20Fidelity - 11/30/13 at 5:53am
HM-601 will drive SR80 just fine, but you can take it further by adding an amp and flavouring the signal from line out. I found HM-601 to perform slightly better from line out rather then headphone out, but for driving SR80 it will to that easily.
Some things to remember when purchasing HM-601:
Battery life is rather bad, I was getting 6-7 hours max running 16/44 FLAC files. (it was never off the charger)
You must number all your files with 01,02,03 infront of the track name or it won't play albums in order.
It gets rather hot when you leave it paused for to long.
Personally, while HM-601 sounded nice, if you get just get the SR80 then look at Colorfly C3 DAP for only $100 I rate it higher (and cheaper) then the HIFIMAN, and the battery life is about 16-18 hours. I think that will give you better sound then HM-601 and C3 amps clean from headphone out with something like the $100 C&C BH amp many members use.