I would recommend Kilimanjaro. They are used to handling private jets. There is a handling company there that will assist you.
From there you can charter an aircraft to Tabora. Northern air has a PC12 which will get you there quickly. You can also try regional air, air excel or federal air.
Don't stay at KIA lodge for 10 days unless you want to go out of your mind. Arusha is much better, more hotels, more things to do. Try out the new arusha hotel or Kibo palace.
If you go to Mwanza and stay there for 10 days you'll also go out of your mind.