(though how that will work when talking about 4 different major airports launching A/C independantly to the same exit points is a mystery to the coalface ATCOs)
It shouldn't be.
Tactical VECTORING, not too dissimilar to approach radar methods, is the answer. At 250 kts you'll find aircraft a lot more "manoevrable" (they cover less ground in turns for instance).
AREA people have to do this in the UK and abroad (with varying degrees of success) daily. e.g. streaming into MAY, AVANT, DPE, MURUE.... corner posts etc , all from different points.
Haven't got "time" to do it? Split the sector. Give yourself more time. You may be surprised what is achievable.
Best Rgds
BEX
a coalface ATCO