What could reasonably be done in case 7,500 airplanes must be landed quickly?
There's roundabout 400 paved runways over 2438 m (8000 ft) in the USA and EU, respectively, and about 200 or so in China and Russia, respectively, so that's about 1200. They are long enough to deal with most aircraft. Some might be untowered or unavailable, but then there are other countries, too. Estimates for "commercial" airports worldwide run around 4000 (there are about 9000 IATA codes, apparently).

So, every suitable runway would have to accommodate around 2 to 10 aircraft. 

You can have around 50 to 70 movements per runway per hour, though you need separation of up to 3 minutes to avoid wake turbulence if a smaller jet arrives after a heavy. Let's say 30 landings per hour, and we're talking about 20 minutes, just in terms of pure runway capacity. 

Now, to get all those planes lined up nicely... Parking might get crowded, too, but I'd think it would be doable - just fill up taxi ways progressively (presumably you don't care about take-offs for a while). See this diagram of aircraft parking prior to the Tenerife disaster (where many planes diverted to the small Tenerife airport due to a bomb in Las Palmas).



At any rate, the practicalities would be daunting. Would be interesting to see a proper feasibility study.