Interesting ideas : a few issues though which need addressing : the random slot drops are there because people had worked out the timetable for releases and were sitting there waiting to clean up : giving a time for them will just repeat the earlier problem. Yep, the idea of limiting how many you can buy has some merit, but it then raise further issues of 'unfairness' ( real or imagined), in that those able to come back in 120mins, or 180mins, or whatever, will be able to, whilst those without 24/7 interweb will not. Myself, I drive long distances for a living, effectively, I'm off-line all the work day : so that would limit my slot buying to only part of the day, assuming the slots drop in that part of my day, and even then, I'll have to break my sleep to come back and get some more (if any are left). If they drop during my work-day, no amount of pre-drop warnings serve any purpose for me, I cant get them regardless. At least the 'random' method maintains some equity, even if it sometimes feels that it just means everyone is unlucky most of the time.
The idea of tying cost to airline size (be that value/fleet numbers) : that already happens, in a roundabout way though ; the more slots you buy at an airport, the more the next costs, which is reinforced by running a large fleet as, naturally, you will have more flights and need more slots.
In the end though, my concern is basing these changes on the experience of HQ-ing at LHR : Thats an almost unique airport in AWS with specific problems related to its size and particular demand levels, though another 10 or so majors have similar issues. The majority of airports in AWS do not have those issues in anything like the same scale : I'd be concerned that adjusting things to suit LHR would add another layer of restrictions on everywhere else that arent really necessary and would only serve to frustrate players who chose not to base at such majors because its a damn pain but now get to endure the cure prescribed anyway..