Assuming they're all in the same class, I think your best bet for totally headset-free would be to only connect one device to a speaker (bluetooth or wired, either should work), then mute the speakers on the other two. Then they can all three still use individual mics, either holding the headset like another commenter mentioned or getting some cheap desktop mics.
I also wouldn't totally rule out more comfortable headsets. Something designed for all-day work, like this, would be way more comfortable than most consumer-oriented headsets.
This is the one work gave us to use when at home
https://www.amazon.com/Plantronics-Blackwire-C3210-Headset-Over/dp/B07CTS6F8K
Otherwise i have used the microsoft lifechats 2000/3000 before and both were pretty good