No problem here 6870 + 5850 in one case (no crossfire bridge ofc)

very very strange   try different versions of the sdk 2.1->2.4

Try the GUI Miner (it's the fastest to set up) also what is the core clock?

[ATIADLHAL]
EnableUnofficialOverclocking   = 1
UnofficialOverclockingEULA   = I confirm that I am aware of unofficial overclocking limitations and fully understand that MSI will not provide me any support on it
UnofficialOverclockingMode   = 2
AccessibilityCheckingPeriod   = 0

Paste this in MSIAfterburner.cfg and save 

Edit: Paste it in place of Default [ATIADHAL]

Btw you should be getting a lot more from your 5850-s. Somewhere around ~340 Mh/s with just clocking the core to 900Mhz, which for most 5850-s doesn't require increase in voltage