Because you sound like you are after gaming fps my recommendation for your $300 budget would be to sell the 6870, and grab a 7950. That would be your best gaming fps improvement with your $300 budget.
Current sale: for $299.99, but $30 MIR and the following included
1.
Never Settle Enthusiast Bundle Far Cry 3 Sleeping Dogs Hitman Absolution Download *AMD Promo Only* (a $170 value!) 2.
Nexusz PC Game Coupon - MSI Promotional (a $50 value!) 3.
Shogun 2 PC Game Coupon - MSI Promotional (a $50 value!) 4.
Dirt Showdown PC Game Coupon - MSI Promotional (a $50 value!) MSI Radeon HD 7950 Twin Frozr III 880MHZ 3GB 1250MHZ GDDR5 DVI HDMI 2XMINI DP DX11 PCI Video Card
Another option, if you are after a more generally fast feeling computer (and load times), is to just keep everything as is and add a 120-240gb SSD. Save the difference for a future upgrade or something else you need.
Keep your eyes open tonight/tomorrow and monday for even better deals.