You may need to take out the middle fan bracket to fit your GPU in.
I've built computers with an antec 900, but none with the longer GPU's.
As for your cpu cooler, I really like using the Tuniq Tower.
But if you go with the Tuniq, be aware that depending on your mobo, you can't attach an extra 12cm fan on the window. I changed mobos for a customer and the tuniq got in the way on the second mobo.
Your CPU cooler you chose looks really similar, so just be aware that the antec 900 gives little clearance to a large cooler like the tuniq tower.
On my personal desktop though, I use the Cooler Master GeminII with 2 12cm fans attached to give better case airflow and to have constant air pushing over my ram :]
One note though, I didn't see any hard drives in your list. I presume you already have a hard drive?
And I don't think you need such a strong PS for even 2 4870's. Something like the 620W Corsair HX would do. But I guess at $20 more, the one you have works too.
A wise one (not myself) wrote recently, "The Antec 900 is perfect for teenagers and disco fans. Flashy lights all over the place. The RC-690 on the other hand looks more dignified, and you can actually sleep even if the PC is on in the bedroom. Apart from that, they're both good cases and will fit your parts." ...I can't help but agree.
I was looking at the Cooler Master Stacker 830 and was impressed. Also I was looking at the Antec 1200 and it also looked like it was good too. I'm wondering if my Xigmatek 1283 120mm rifle cooler will fit in the Stacker.