Can you run a quick test, turn on local monitoring?

[StuartR]

What would you expect the effect to be of running with local monitoring turned on.  Others in your session would sound like they're behind you, I'd presume, since you're getting the direct signal from instrument/mic into your headphones without even going through jamkazam or your computer.
I confirmed today that turning off the local "faders" on my device does not enable my personal mix sliders.
So leaning towards a Mackie ProFx 6 channel, or something very similar.

I think you've answered your own question. The whole objective of playing with others through the Internet is to keep the latency as close to being in the same space as practical.

Yes and this probably explains why it seems our main vocalist appears, to me anyway, to sing behind the beat consistently.
As to the Mackie option, the big spreadsheet in these forums shows it at 13ms latency ---- I realize this varies highly by environment, but that's twice what I'm showing with my current device.

Not sure you told us what platform you were running on but on a Mac with Thunderbolt 3 ports or a PC I'd recommend a MOTU M series. Latency around 3 msecs.