Update: I installed macfanctld but still saw issues. After some playing, I noticed a correlation between my internet connection and a windows 10 pro HP EliteBook 8470p connected to the network. Whenever it would connect my connection would hang. All my connectivity issues seemed to happen while it was online. Looking at iftop more, I saw it sending frequent packets to 255.255.255.255:17500, which is supposed to be dropbox, and a few occasional pings to some DNS servers as well as 192.168.1.255.
Attempts to firewall port 17500 and later the laptop's ip address through ufw proved pointless. I even uninstalled dropbox on the owners laptop but still saw issues, even when my computer wasn't detecting any traffic from the other laptop at all (after disabling the firewall, of course). I suppose there could be some sort of frequency conflict between the two, I haven't monitored the internet on the other laptop, but the user hasn't expressed any frustration while using it so I'd assume that's not an issue. Also, using a combination of tcpdump piped to ts, I verified that traffic from port 17500 would be received but wouldn't print out to the console for up to two minutes while my internet was hanging (tcpdump was in --immediate-mode so it shouldn't have been a buffer issue). Because of this, I think there's some sort of issue in the physical processing of the packet inside of the broadcom chip causing the delay after it's received. Hopefully all of this information is helpful to anyone trying to debug the issue. It is definitely linux driver related as I saw no issues when using Mac OS. I don't know the code well enough to make any further suggestions, but I'm afraid the issue is probably hidden in the proprietary libraries. It'd be nice if I could revert back to the broadcom-wl sta driver rev 6.2.155.19. According to http://www.hackermusings.com/2013/02/better-wireless-drivers-for-the-bcm4331/ that one contained a fix to the issue. That one was so long ago I doubt it would work though. Given all that, I think the only way to "solve" the issue is to buy a wireless USB dongle.