I wouldn't trust that unit with 7870 crossfire and an overclocked FX-6300. It doesn't have the required four PCIe connectors, and it's not good enough quality that you could safely use molex to PCIe adapters, given that it is a multi rail unit. (Putting graphics card type load on a rail designed to power things like fans via peripheral connectors may overload the rail.) How old is the PSU, by the way?
I'm wondering why you want to crossfire that card? For one thing, your CPU needs upgrading before it can take full advantage of a graphics card upgrade on 1080p resolution, and secondly, I think it'd be a better idea to sell the 7870 and upgrade to a 280X. That would not be as great an upgrade in terms of pure framerates, but you would avoid any and all hassles resulting from running two cards: noise, heat, power consumption, lack of connectors, microstutter, lack of Crossfire profile, inconsistent performance compared to a single card.
Another issue that I see is that your motherboard doesn't support PCIe x8/x8. It has two PCIe 2.0 x16 slots, but the second one is electrically limited to x4 bandwidth which limits the performance of a graphics card installed in that slot.
So given the fair chance of CPU bottlenecking and the lack of proper Crossfire support on the PSU and motherboard fronts (not to mention the disadvantages of Crossfire itself), I don't really see any other option than to return the 7870. If you want to upgrade, a 280X would be a decent option although it may also be bottlenecked by the CPU in some games. The best option, if you can afford it, would be to upgrade to Intel Haswell i5 and a 280X or even a 290.
I think yours is 80+ silver, so its not some piece of junk PSU like most that are out there; and companies tend to exaggerate power requirements to be on the safe side.
Efficiency doesn't really say anything about reliability, although efficiency and reliability may have
some correlation. Also the ModXStream 600W is 80+, not even Bronze rated. Says so right there on the Microcenter page the OP linked.
The unit is by no means high quality. It is alright, but not alright enough to use molex to PCIe adapters. Despite the 600W label, the +12V output is actually only rated for 504W, and it can
just barely output its rated wattage, which means it is definitely not designed for continuous 600W output.