2x users, 2x iOS devices, 2x apple TV (3rd Gen) over airplay

Advice very welcome. I am new to Zwift and have been using and enjoying the community for the past 2 months. My set up in the garage has been a Wahoo Kickr Core broadcasting Zwift from my iPhone 8 over airplay to a Apple TV (3rd generation unit). It’s generally been working fine.

We’ve enjoyed the Zwift so much we have duplicated the same set up: this time with a Tacx Flux S smart trainer, an iPhone 6, broadcasting to a second Apple TV (3rd Generation) on a second TV.

All good in theory but I can’t get the two sessions to run concurrently. One session will load up but the other hangs. Where I have got both working in Watopia at the same time it is a really stuttering picture. Where is this breaking down? Is this setup workable?