Just thought I'd bounce in here and offer a couple things I've picked up. Like you ladlon, me and a couple buddies are newbies (a week in). When reading your OP, I knew exactly what you were talking about, and judging from several of the responses; I guess we're all in this together (when it comes to grass).
Anyway, in respect to grass, I feel your pain. But I guess there's a couple things I've sorta picked up that make it a little better.
First things is something somebody noted in this thread, but I think I'll kinda push it back up to front of the line to kinda underline it: 3rd person perspective.
I'm a big MMO player, so I'm more than comfortable with 3rd person perspective (usually), but I definitely do NOT like it in FPSims. BUT! It's pretty useful when you're lying in the grass. You still end up panning the camera down to ground level (which usually is again; obscured) to fire your weapon, but at least you can sorta tilt the camera a bit and get a clear(ish) view of what's over the grass. At the very least, it might allow you to see a better spot to move to. So far I've been liberally switching back and forth between First Person and 3rd Person Perspectives when I'm in the tall grass. I just might try to force myself to get used to 3rd Person all the time, because your little avatar does look cool as hell runnin' around out there, plus there is some increased situational awareness in that view.
The second thing is something I'm sure you've already learned just from trial and error: find a better spot. I know that sounds dumb, but I guess to put a finer point on it: find a good spot BEFORE you hit the deck. That's what's sorta been workin' for me. Time doesn't always allow for that, but just kinda have it in the back of your mind. It helps.
I always move crouched, so my perspective is sorta close to the ground and I just kind of have like a check list of things I want to do (avoid open ground, move to cover, figure out where and what I'm gonna do with the squad, etc) before I break cover and move to my next firing position. And one of the things is "what patch of ground is gonna give me (hopefully) decent breaks in the grass to have eyes on the target". As you mentioned, I'm usually looking for any bit of elevation to take advantage of. Good ground is everything. But I also try to do a little mental geometry or billiards in my head where I try to look at some patch of grass and say "ok, I think if I lie down facing that way, and if I draw a line between those tufts of grass towards what I think I'll be able to see through the grass..." stuff like that. I'm usually wrong, but I'm starting to surprise myself with the occasional sweet angles.
But of course, maybe the things that trumps everything in this is: in my little check list, being forced to lie in a field of grass is like LAST on my list of tactical choices (for obvious reasons). :p But, sometimes ya just have no choice.
Ok, I'll stop babbling now.