How's this $1000 build?
Minor edit to change the ASUS 7870 to the Gigabyte 7870 which I prefer.

If you do not plan on overclocking, I would stick with the stock cooler and grab a
E3 1230V2 from NCIX for about 255 which is only about $30 more than the i5 3570k. This is about the cost of the CM 212 EVO. The 1230V2 offers more cache and Hyperthreading for cheaper than the i7 3770 ($300). The Hyperthreading and cache will help in the recording and vdieo editing alot. It will also be better (assuming same clock speeds) than the i5 since battlefield 3 multiplayer actually scales to 6 cores. The e3 1230v2 can also be overclocked in the future via the turbo multiplier to about 4.1ghz 1 core, 4.0 on 2-3 cores and 3.9 on all 4 cores at load.

I was not able to change the i5 to the E3 1230v2 since its does not show up in pcpartpicker. FYI i checked the AsRock site and your board supports the E3. The E3 1230v2 is like the hidden gem of the Xeons =P