I personally had issues getting my Pi sticks to run 6-8-6-24 @ 1600, but I assumed that was because the timings were rated for intel and I was running on AMD rigs. That said..... 7-8-7-24 has a fair bit of headroom over and above 1600.
You mentioned setting the 6-7-6-24 in bios, and then leaving everything else on auto.... did you bump the mem voltage up to the required level? If they're the same sticks as I've got (dual channel set rated for 6-8-6-24) they need 1.6V to run at those speeds.
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