Yeah the fire is really pesky for recording. It's noisy, right in the way, and any musicians on the far side of it are beyond good proximity to the mics.
Four or more cardioids in a close ring around a fire facing outwards towards the musicians could work better, with good rejection of the fire noise while keeping the musicians more on-mic, but that's ridiculously complex for a campfire jam, places the mics and cabling uncomfortably close to the fire/smoke, and would end up pushing the circle too wide.. just doesn't seem a good solution. Instead, herd the jammers under that typical 10x10' square pop-up canopy which is probably set up close by-
Recording a jam circle underneath a pop-up canopy is far, far better. The musicians naturally huddle in closer, the reflection off the canopy provides good close-reflections which makes the sound richer and more present sounding. And that focuses the sound from the core group in the center around the mics and slightly lowers the level of the talkers around the outer periphery the circle. The mics can even be suspended from the overhead canopy frame, avoiding the need a stand in the center. And if it may rain, everything is protected, and the jam can continue.
I plan on doing exactly that with the Tetramic. It's so small it won't be imposing hanging in the center, and it's ability to decode any number of virtual microphones of any pattern, pointed in any direction, after the recording has been made, should work really well in the center of the circle.