Yes, the idea in the Exchange French is that Black can simply develop in an assymetrical way to White and get good counterplay that way.  If White castles K-side, Black castles Q-side, etc.  The central file is easily covered by minor pieces, so the rooks aren't easily exchanged.

In reality, I get less counterplay as Black in the French Exchange than in any of the other French lines I play.  I don't mind this; I like endgames, and people who play the Exchange against me are almost always weaker players.   

But it might fit very well into the idea of a "d4 opening that limits counterplay by Black".  Certainly if you're comparing Black's counterplay in the Dutch to his counterplay in the Exchange French, I'd have to say the Dutch wins hands down.

Thanks for explaining to me what  Iljin-Zjenevsky is, I never play the dutch, so I didn't know...

Why wouldn't french fit into "limit counter play for black"? The exchange variation in it might be ideal.

As a Kings Pawn Player I think that 1.d4 e6 2.e4! is a very strong move. 

For 1.d4 players looking for something interesting and more in the Queens Pawn spirit against 1.d4 e6, then maybe 2.Nf3 f5 3.d5!? fits the bill.

Tops 

The Iljin is basically the Classical Dutch.

Of course with 2.Nc3 or 2.Bg5 The leningrad, Stonewall and Classical Dutch are all made redundant.

Toppylov 

I'd like to toss in a word about the Slav Exchange as limiting Black's counterplay.  I studied and have won several nice blitz games as Black using the following opening:

1.d4 d5 2.c4 c6 3.cd5 cd5 4.Nc3 Nf6 (if Nc6?! White can play 5.e4!? and get a good game) 5.Nf3 Nc6 6.Bf4 Qb6!

I don't claim that this is a refutation of the Slav, or even a brave new idea.  Rather, this move forces White to play accurately and actively or risk being over-run.  I don't think there is such a thing as an opening that denies Black counterplay.  Well, there is one:  If you are much higher rated, it's the last round, and your opponent needs a draw for a cash prize, 1.d4 (draw) may do the trick.

Its laudable to want to limit Black's counterplay, but impossible to extinguish it entirely.

Your Fianchetto against the KID is a good choice for the positional player.

Against the Dutch I think 2.Nc3 or 2.Bg5 are good solid choices and although the games can become sharp I think they are easier and more pleasant to play as White.

Against the Nimzo, 4.Qc2 is a safe and solid choice from what I remember.

Against the Queens Gambit you have the annoying risk free exchange variation as you do against the Slav.

Providing you play 3.Nc3 it is not clear that the Benoni is even playable, it all depends on the current status of the Flick Knife Attack, or failing this the set up with an early h3 and Bf4 used to be quite effective.

Against The Budapest 3.Bf4 is safest.
Against the Albin's Counter Gambit 5.Nbd2 has a good solid rep.

Of course I am not a 1.d4 player but some of the choices presented above should be anaemic enough to suit your tastes. 

Toppings    

"I'm looking to build an opening repertoire around 1. d4 openings that limit counterplay for black."
This kind of player is exactly the reason I decided to pick up the Iljin-Zjenevsky. In this opening Black always has  counterplay; the only question is if it's enough.

Fair enough, but I see trouble with this plan after 1 d4 Nf6 2 c4.  Black can steer toward his/her favorite Indian and it seems difficult to completely limit Black's counterplay after 1 d4 Nf6 2 c4 e6 3 Nc3 Bb4, for example.  There are quieter lines, to be sure, but Black will surely have some counterplay.  Same goes for the King's Indian after 1 d4 Nf6 2 c4 g6 3 Nc3 Bg7...