I have the Leatherleaf Sedge - the 'brown' stuff, to which you referred. I don't have any pictures to post at the moment, but can tell you what I have it planted amongst.

It's in a bed out by the end of our driveway - this bed contains mostly xeric-type plants which don't require much attention.
In the immediate vicinity of the sedge is
'Elijah' blue fescue,
'Dragon's Blood' sedum,
'Ruby Star' coneflower,
'Blue Bedder' salvia,
'Mexican Bush Sage',
'Autumn Joy' sedum, (the sedge looks particularly gorgeous next to the foliage and reddish/copper flower heads of the AJ sedum)
a large clump of pampas grass, several varieties of lavender, and there are others, but do you see a color theme going here? The bed is mostly plantings in various shades of burgundy/red/lavender/blue/blue-green..the coppery (not brown) tones of the sedge fit in perfectly with these colors. It really isn't a 'tricky' grass to incorporate at all...wasn't for me, anyway. I guess, if not planted correctly, it can look dormant and rather dead, though. You need companion plants which enhance the coppery tones of the sedge, rather than make them stand out and scream BROWN. If planted properly, the sedge looks more coppery-pink, than brown. Also, it needs to be planted in groups of 3 or more, or it really does look just like a clump of dead grass.

If I think about it today, after my daughter goes down for her nap, I'll take a few pics. of the sedge I have, and post them here for you later on this evening.
BTW, I've seen the stipa planted en masse and it was quite lovely. However, I don't have experience with this particular plant, so I can't comment on any invasive qualities.

Renee