I've heard good things about Tanzania but haven't partaken. I can tell you that there are many nice flycamps in Zimbabwe that would be very traditional.
Some examples:
Tuli Circle on the Shashe river touching the Botswana border in SW Zimbabwe. Very nice. North, South and Pakenham camp are all just what you're looking for.
In the north as part of the Mana Pools area you have Chewore, Nyakasunga, Sapi and other camps that are very much traditional fly camps.
In both cases, there is usually (but not always) a permanent toilet/shower room and a permanent lockable storage room for your food. Most have a concrete poured braai and little tiny shelters for the government game scouts. The only other amenities that you do want would be a skinning beam to take care of dressing the game and a lockable fenced area for salting your trophies.
The hunters and staff are all in traditional fly camp accommodations with these exceptions above and you'll not see any other structures (save maybe a water trough windmill every 15 miles of wilderness).
Tanzania, Zambia, Zimbabwe and Mozambique all sound like they have the type of experience you're looking for in your safari. Happy hunting!