Try contacting Safari Infinity. https://safari-infinity.com/
They are a local and Tanzania only operator. They will be able to put together a customized itinerary for you with your own vehicle and driver. I've found them to be responsive and have put together a great itinerary for our family and budget. Much more customized and smaller camps.
We are doing 2 nights near Kilimanjaro for some day hiking, 2 nights Tarangire (Kichuugu Camp), 1 night Karatu (Gibb's Farm), 2 nights Ngorongoro (The Highlands), 2 nights Central Serengeti (Nyumbani), 3 nights Northern Serengeti (Mara River Tented Lodge), then flying back to DAR (I think). In June you will probably want to go to the Grumeti portion of the Serengeti instead of the North.
General advice is to contact 3-4 with same requirements and see who is responsive and fits your requirements best.