How can I high pass (DSP) filter a low frequency signal without introducing lag?
I'm afraid you're up against a fundamental limitation of real, causal physical systems. You're asking for a filter that can distinguish between signals that have periods of 12 to 16 seconds, but only allowing it to "look at" a 2-second segment (1/6 to 1/8 of the period) of the waveform in question. It simply isn't possible to get no phase shift and low delay under these circumstances.

Can you provide some more context for this problem? What is the nature of the signals, and why is such low processing latency required?