You could do it with a 4 channel mixer and USB audio devices hooked up to one Bluetooth transmitter... I don't know about latency though and good luck with the cable management!

Rolls MX51S Mini Mix 2 Four-Channel Mixer https://a.co/d/48XLqLi

USB to RCA https://a.co/d/iam01Xj

Bluetooth 5.0 Transmitter 3-in-1 https://a.co/d/47TuAMn