You will be a complete hero if you write up how to do "blind signal separation" with an economical microphone array. Such a device can be ceiling mounted and use copious heaps of mathematics to locate speaking people and isolate just their voice, attenuating other room noise and echos.
There are likely affordable hardware candidates, the $55 ESP32-Lyra-TD development board with 3 microphones or the MATRIX Voice with 8 at $75. Both have special hardware for the signal processing.
* Poor frequency response
* Only one channel
* They pick up mains 50/60Hz hum and other disturbances from power electronics
* works best when whole room is inside the wire loop, which isn't always possible. Portable "wireless" systems exist but have range at most few meters.
Advantages:
* technically very simple, reliable, not encumbered by patents
* most hearing aids have the receiver coil
...and this is why hearing aid manufacturers hate it. They prefer to sell proprietary devices. There were attempts to move to FM radio but as everyone does it differently and both transmitters and receivers are expensive, it isn't widely used. Newest hearing aids come with bluetooth, I've no idea whether it can be reliably used this way (simultaneous streaming to multiple bluetooth devices).
What I am about to write here is similar to third hand information.
I do not have first hand experience.
I looked into putting an audio loop into a venue. I asked an audiologist
about the prevalence of T-coil equipped hearing aids. She told me most
users prefer small and rechargeable. There is not much space in the unit
and rechargeable would likely be selected. So, the T-coil does not get
included. She thought T-coil units were common in Europe.
There are special amplifiers to drive the audio loop. The makers don't
tell us much about them. I think we would call those transconductance
amplifiers. Reading the subject article is encouraging. Perhaps we
will just try this after the virus is not such a threat.10-20 years ago everyone had a T-coil and loop systems were a great option. Now they're not.