So, sort of interesting update.
I moved the 980ti to PCIE slot #2, which is x8. And doing that seems to have solved a lot of problems. Latency is much better now as measured by latencymon, and I was able to play Battlefront and WoWS for a little bit without seeing any of the sort of drops I was getting before (and no latency spikes either). Now that I'm running 2560x1440, I'm getting a solid 100-110 fps at Battlefront with everything maxed out and running the CPU at 4.5ghz. (Which is really nice with gsync, btw.) Haven't tried BF4 yet, but I will report back once I do.
This seems to me to be a lot closer to the sort of performance I ought to be getting? Am I still missing something here? What, if any, performance am I losing by running in the x8 slot rather than the x16 slot? Seems to be that the motherboard has some issue with that slot?
Thanks again to everyone who has helped out!
You've got something else sharing resources with the that primary PCI-E slot that should not be.
I had a similar issue. I record my own music. I recently made a change to use the builtin Firewire on my Motif XS synth workstation, since my motherboard also has builtin Firewire. Immediately, I noticed degradation of quality, including pops and clicks introduced into the audio stream. Latencymon reported AHCI drivers and network drivers as the issue. I struggled with it for a while, until I discovered the following.
I was using Marvell SATA 6 ports on my motherboard. I found that they were both sharing IRQs with my video card, the Firewire port, and my LAN port. I disabled the Marvell SATA ports (which are garbage, BTW), moved my HDDs to the onboard Intel ones, and then let the motherboard rediscover the hardware. Now, everything is on its own IRQ. No more pops and clicks.
Check your motherboard manual. It should have a chart which shows what PCI-E slots share IRQ resources with other things. Disable and/or move them around accordingly. You should not have to run your video card in that x8 slot.