Best communication scheme for a battery-powered Bluetooth LE display?
You have several questions piled up here, coming short of simply asking "design this thing for me, so I can sell it to you better"...

Anyway, Re: power saving, the simple approach would be to synchronize clock on your device with the one in smartphone at the time of pairing. Then you would attempt to re-connect at set intervals and for brief time only, thus saving power. Re-synchronize clocks on successful connections.

Furthermore, if smartphone does not have any new data it can simply skip the session without establishing connection, which will save a bit more power too.

Re: interference, shouldn't SSP take care of this for you? And if that is not enough you can include some kind of GUID encrypted with time-varying cipher (good use for synchronized clocks) into handshake.

Re: Security, the security of the connection itself is pure software problem, coming on top of encryption (which is mandatory for 2.1 specification). Since you own the high-level protocol on both sides you have an option to make it as secure as possible.