To be fair to my colleagues at EDI, the landing rate there is largely outwith their control once they get into a holding situation.
The Scottish TMA was never designed to permit any "real" holding (think back to a couple of Tridents a day). When the all-too-common barrage of EDI traffic arrives at the Talla sector (126.3) the radar controller is really working his nuts off and simply processing the traffic through the Tweed hold slips down the priority list as they sort it out. This is why (I would imagine) you end up with the situation you describe.
Edinburgh radar has modern equipment and will almost always have both radar and final director manned (or at least available), so if the traffic arrives in the right order through Tweed it is possible to acheive a very good landing rate.
This situation should be eased somewhat when the Scottish TMA is further split; I understand that this is imminent.
From the airfield point of view, bear in mind also that EDI doesn't currently have any RETs so they can't "pack" (i.e. 3Nm or vortex) like some airfields can, but on a mixed-mode runway that's generally not possible anyway.