1. Why cannot the STARS continue pass LANAK, and feed directly onto final for 05 & 23, with defined speed control to provide the necessary separation?
As you said yourself, think outside the box .... EDI jet departure SIDs climbing to 6000' pass across the extended track you propose after LANAK. You'll no doubt want to be descending out of the FL equivalent of 7000' after LANAK as part of the STAR, so what's your separation there if both aircraft lose comms ??
The current setup is a safe one. Glasgow bring you on in a controlled manner, descending with cognisance of other traffic in the TMA area, and the Galloway sector at Scottish climb the EDI departures to jump the arrivals who they know will be descending to cross the sector boundary North of LANAK below an agreed level under the control of Glasgow. If it's all looking a bit complicated for ATC, there is the backstop of holding you at LANAK, an option which is not automatically there with your proposal.