You misunderstand some principles of networking here.
I hope you won't take offense if I clear a few things up.
First of all, reserving an IP address in the DHCP table, and configuring an iP address manually are two different things.
I have never seen a case where reserving an IP address in the table did not work, except in a very old router that didn't work properly when reserving addresses. (this is not an atypical way for routers to fail or become flaky.)
If you reserved it in the DHCP table in the router, configuring it manually was completely unnecessary but harmless.
The device asks the router, "IP address please." and it always sends back the same one. Normally it's good to reserve the one it's already using in the table but it doesn't really matter.
Anything outside the router's range of IP addresses it distributes can be assigned by you manually on each device but that gets really tricky.
In fact, what may have happened here is what's called an IP address conflict, where either another router is giving out IPs, or a device is configured manually for an IP address in another router's range.
I would recommend switching the apple tv back to dhcp. I think you'll find that it stays fixed, and is a cleaner over all setup.
As for the ethernet cable, if that bothers you you can use either powerline networking or MoCA adaptors but I haven't tested either, but I bought a book on cord cutting by GigaOM and it recommended it.
Also, test latency.
edit: if you have it configured manually and reserved, that is an ip address conflict. do one or the other.