Well it took a year of owning this laptop, but I figured out how to kill the constant and quiet-but-audible static in the headphone port.
@RebelMoogle alsa has a setting for my sound card called "Headphone Mic Boost" that I can set between 0 and 3. It needs to be set to exactly 1. 0 is the default and has quiet static, 2 has loud static, and 3 has deafening static. 1, for reasons I'm not even about to start asking about, has no static.
@RebelMoogle I for the longest time assumed it was driver issues, but my friend with the same laptop as me and a similar setup has never had a problem. I tried tweaking every tunable I could find aside from levels on the sound card (didn't realize "headphone mic boost" mattered, my headphone doesn't have a mic).
@dgonyeo huh interesting, and weirdly obscure. I should try that on one of my computers.