You probably should try to do it old analog style: just plug your microphones into each other’s PCs and set up soundcard's mixer to add mic input into the mix
Did you try a local mumble server? Haven't played with it for a long time but last time it was much faster than teamspeak and we used it happily at home sitting next to eachother. That and get better headphones that close out sound from environment :-)
Our computers are beside each other so we need to use headsets, it's important to hear 360 audio for footsteps and other sounds in shooters.
We need to hear each other, game audio, teammates voices, and each other's voice.
Our voices can sometimes bleed through the headsets so we need there to be little to no lag to reduce reverb.
Plus the faster our voices reach each other the faster we can react to the command / callout.
We can't use voice channels in the game, discord, or anything that goes over the internet.
Currently we use teamspeak with a local server, which works well, looking to reduce it more.
Sometimes we simply play with one headphone ear partially off, but that ruins the surround sound.