I'm rated about 2175 USCF, and play mostly people in the 1900-2350 range, so take that into account with my following comments.

While I'm a life-long 1.d4 player, I have the same problem of finding an edge against the Grunfeld.  Fortunately, I face it over the board very rarely.  I also play 4.Bg5 sometimes, but I don't think it's that great.

The variation that I have scored best with is 1. d4 Nf6 2. c4 g6 3. Nc3 d5 4. cxd5 Nxd5 5. e4 Nxc3 6. bxc3 Bg7 7.Nf3, because most opponents actually now play 7...0-0?!, which is certainly dubious because White can play 8.Be2! instead of 8.Rb1.  There is some nice analysis on this in Yermolinsky's book The Road to Chess Improvement.  Basically, compare the position after 7.Nf3 0-0?! 8.Be2! to 7.Nf3 Nc6! 8.Be2?! and you'll see the difference.  Many fairly strong players (USCF 2200+) mess up this move order, maybe because it's not explained in many books that cater to the Black side???

Anyway when my opponents play 7.Nf3 Nc6 I play 8.Rb1 and I have decent practical results, but there is so much theory there that I can't keep up with it all.

One line that I think is quite promising for White is 1.Nf3 Nf6 2.c4 g6 3.Nc3 Bg7 4.d4 0-0 5.Bf4!? d5 6.Rc1!  I can't usually play this way because I play the Saemisch against the KID (so I don't want to commit the King's Knight to f3), but if I'm certain I'll face the Grunfeld I'll sometimes use this move order or something similar.  The main point is that one of Black's main ideas in similar positions, 6...c5 7.dxc5 Qa5?, is now a mistake because of 8.cxd5 Ne4 9.Be5!  If you put the Knight on f3 vs. the King's Indian and Benoni, I'd recommend giving this variation a try.  Another line you'll face a lot is 1.d4 Nf6 2.c4 g6 3.Nf3 Bg7 4.Nc3 d5 5.Bf4 0-0 6.Rc1! dxc4 7.e3 c5 8.Bxc4 cxd4 9.exd4 +/=, when you have the Black side of a QGD Tarrasch with two full extra tempi.  In my opinion, these 2 tempi are sufficient for an advantage.

Good luck...

The critical test is still the 8.Rb1 line, but lots of work is required.
Up to a certain level the Keres-line is quite handy. 4.Nf3 Bg7 5.e3 0-0 6.cd5 Nd5 7.Bc4 Nc3 (7. ... Nb6 8.Bb3) 8.bc3 c5 9.0-0 Now lots of player move automatically 9. ... Nc6 and white gains a plus after 10.Ba3. 9. ...Qc7 is the correct answer, but even 2200 elo players often don´t know it.

Perhaps the Brinckmann Variation would be a suitable choice - I am referring to the position after 4.Nf3 Bg7 5.Bf4 0-0 6.Rc1. After 6...c6, White has an improved Slav Grunfeld because his dark-squared bishop is actively positioned on f4, and the 6...c5 variation is currently +=. 

The critical variation is 6...dc4, when both 7.e3 and 7.e4 lead to complicated, tactical positions that should suit most 1.e4 players. You can alternate between both moves to keep opponents guessing. 

Otherwise, I would suggest the Russian system with a delayed Nf3, ie 4.Qb3 dc4 5.Qc4 Bg7 6.e4 0-0 7.Be2!?, which probably isn't any better than the 4.Nf3 Bg7 5.Qb3 move order but is tricky, and many of your opponents would not be familiar with the intricacies of this line.

OK, typically I don't like threads like this, but I'm hitting a road block. I'm a 2300 USCF rated player who's trying to improve, played 1.e4 most of my life but sometimes have gone 1.d4 to spice things up. I'm thinking about making 1.d4 more than just a once-in-awhile thing, but I don't know where to start in looking for a line against the Gruenfeld.

Other 1.d4 defenses are not causing me as big a problem. Most of them I at least have an idea what I want to try. But NO variation against the Gruenfeld appeals to me!

I think part of the issue is that, as an 1.e4 player, I am not used to having a big pawn center. So += positions just look like = to me. The funny thing is, the KID should cause me the same dilemma, but it doesn't. Probably because I am a KID player as Black and know what the KID player fears. 

I've scanned almost all the variations on ChessPub, and some things that I have noted are:

1.) White is having a hard time proving a theoretical edge in the Exchange with 7.Bc4.

2.) The Exchange with 7.Rb1 has maybe too much theory for me to learn.

3.) The Russian has the same problem as I addressed earlier: the big center.

4.) The Fianchetto lines don't look particularly scary for Black.

5.) And now the point that brings me full circle: I don't think White can play for an advantage in any of the sidelines like Bf4, or e3 etc.

Currently I'm fiddling around with 4.Bg5 but I'm not sure in a real otb game I'd like being down a pawn so early, but so far it seems to have more of an 1.e4 feel to it than any other line.

Anybody have any suggestions? Any similar experiences? Should I just go 1.e4 against people if I know they play the Gruenfeld?