Good Day Guys and Girls

We are planing a Bots camping trip next year July 2020, 8 Adults 4 Vehicles, the plan is to woodland, Maxi Pan, then on to South Gate, 3rd Bridge, and then on to Savuti, and Linyanti before going to Kasane,
We are have problems with booking camp sites from South Gate to Linyanti. no campsite available ??
Any recommendations or maybe a different route

Many Thank