I have a similar configuration. I am using Linksys PLEK 500 power over ethernet modules, and a Linksys gigabit switch to drive several components (including streamers Sonore microRendu and Bryston BDP-1) with Roon remote on my iPad. Roon Core is in my office on an iMAC, and connected to an ASUS router. I do not have issues with dropouts or the system going to sleep on me. I am only running PCM files, normally not higher than 24/96, but do 24/192 OK as well. I have one PLEK on the router side, and two PLEK 500s on the media room side using different outlets. One runs my music system, and the other a Sony PC. The PLEK 500s are pretty beefy for POE…They might work a touch better than the ones you are working with.
If you can run a ethernet line that would work best. Other wifi solutions such as EERO are available for whole house wifi which might be helpful. A wifi bridge might help to.