So you want to put the aTV by the TV, but the receiver is in a closet "far" away, meaning you're sending the video signal there and back?
every step will introduce a bit of delay, so if you're converting to cat6 and back twice, in addition to going through the receiver, you're going to have to closely manage the lip sync on the TV.
Have you tried putting the aTV in the closet?
** It might just work. Since the remote works over bluetooth, you might be able to position it so it can still "hear" the siri remote coming from the other room. You'll want to get it against the wall closest to where you will be using the remote, and as far away from other electronics and cabling as possible to avoid interference . Having all wifi turned off on every device in that closet can help, since 2.4 wifi and bluetooth can interfere with each other.
Not sure of your layout, but the aTV doesn't have to be right by the TV, you might be able to position it somewhere else in the room using a shorter regular HDMI cable, it might be behind you as you sit on the couch, but that doesn't matter.
**If all of your equipment (receiver, TV, and extenders) supports HDMI-CEC, you can use the TV remote to control the aTV, it should send the basic commands, (4 directions, enter, back, forward, reverse, pause, play). I even have one app on the aTV that supports the 4 "color" buttons seen on most TV remotes.
The receiver should forward the commands it gets from the TV to whatever source is selected.
Meaning you can put the aTV in the closet, and then use the TV remote to control it over the HDMI cables
**The remote apps on iPhone and Apple Watch control over the network, so those will work no matter where the aTV is.
**The newer aTVs still support the old apple IR commands, so you can use an IR repeater, and still be able to control the aTV in the closet. Most remotes that have pre-programmed codes for other devices have the apple codes built in. you can use the older silver or white apple IR remotes.
the aTV can also learn the commands from any IR remote control.
it looks like
this adapter from jTech does support CEC, as well as IR repeating, 4K, and HDR.