The biggest problem with both slots and the UM is that it encourages people to pool their calls, that there is a large advantage to be had by being online at the right time, and that airlines will hold planes or slots for their friends to get them.
Ideally, there would be much less randomness, and there would be much less incentive to hold things for others. The obvious way to do that is to not make planes/slots immediately available to everyone.
So, in slot controlled airports, the way to do it would be:
At the start of the world, make some number (say 20% of default, or 6/hr, something like that) available to the outside world. For airlines HQed in an airport, they each have access to their own 1 slot/hr. For the first 6 months, that is all that is available. 1 slot/hr, 16 hour day gives 112 slots for the week, that's enough for 21 LH planes, more than enough to get your airline up & running, and profitable.
So, after 6 months, that'll be ~12 slots/hr in use, 50% outside. Can see a couple of ways to do things after that. First, have all slots disappear from public view at that point, and have people put in requests. Think that'll be cumbersome, hard to do an algorithm for. (Think it'd be very good for the used market, that once a week, an airline can request 3 planes of whatever type, and every monday the brokers would allocate planes to airlines. Doesn't mean you get the 3 you want, if there are 200 requests for an a330, there might be 50 offered at a very large markup, if there are only 5 airlines requesting 3 747s each, then all of them would be handed out. Would remove much of the luck aspect, would remove the endless wait for fleets with only a very small number in storage to appear, etc.)
Second option, which would likely be easier to work with, would be basically like LemonButt's idea of terminals. After 6 months, all HQed airlines go up to 2 slots/hr. After 12 months, up to 4/hr. 18 months, 6/hr. And after that, if an airline wants more, they'd need to pay for an upgrade. Slots for outside airlines could stay at double the average size of HQed airlines (so after 18 months, 12/hr), and can't grow past some number no matter how bg the HQed terminals get, say 50% of 2010 default slots, so ~20/hr for LHR/FRA/AMS, 40/hr for ATL/ORD. Biggest benefit to this is it would allow airlines to actually start in an airport mid-game, which is very important for long gameworlds. Current JA, think there were only 3 day 1 LHR airlines, and only 1 of them serious. So by the time others got into the world, it was too late to be able to start there. In fact, after a year, AMS was the only one of the top dozen or so airports to have space for a newcomer. This way, if someone has BKed, their 'terminal' is empty, and so anybody can start a new airline or open a base, and be guaranteed of at least 6 slots/hr to get them up & running. Slot costs would be the same as now, but instead of using how full the airport is overall, it would use how full your own section of it is, so the costs to buy slots would stay roughly the same as now.
Also, on the first monday of each year, or just on Jan 8 if that's easier, all airlines would have to pay some amount for every one of their slots in controlled airports.
We'd have more sustained competition, we'd remove the ability to squeeze airlines out, or prevent their expansion, with slot hogging, there'd be a lot more viable airports for people 5 years into a game. Balancing the costs associated with expanding your terminal ould be the biggest challenge, to make it actually be a considered decision to open up, without it being so big as to be impossible (at least to start with, if it increases to impossible levels when you have 30 slots/hr yourself, then fair enough) or so small as to be trivial (as current slot costs are after you get beyond that initial expansion period).