Pierre,
There are many areas where the civil military handovers work fine. Once prenoted the aircraft is "frecalled" (continue with for those military reading) if clear of confliction. I can think of many areas where this already happens. LATCC Mil - Newcastle/Teesside, LATCC - several military units, Birmingham- Swanwick, Yeovilton-Bristol/SOTON. I am sure other posters will come up with other examples.
In virtually all these cases, the units concerned have talked to each other and agreed the handover criteria to allow these transfers to take place. It is not an insurmountable problem.