My wife and I did a ten day safari in Tanzania earlier this year. We traveled IAD-FRA-ADD-JRO and return, business class, *A award, so two stops rather than the one you prefer. To my recollection, one stop options from NYC are via AMS (KL), DOH (QR), IST (TK), and there may be others with which I'm unfamiliar. I wouldn't worry about safety of overnights in IST compared to places like CAI or NBO. Personally, would stay away from CAI right now. We decided to avoid NBO though we had sufficient miles and availability for two F tickets IAD-LHR-NBO return. Subsequent events have confirmed this to be a sound decision. Arusha is less than an hour by taxi from JRO airport so your safari provider can arrange pickup if you fly in there.

With the miles you'd need for two premium awards, you're likely looking at your Chase or AA accounts for the air aspect. I'm not familiar with Chase Rewards airline transfers so won't comment on routing choices using those points. AA could work through DOH but I have some recollection that two awards may be needed if connecting in the Middle East on AA awards.

Was the trip of a lifetime for us, and we are seasoned travelers. Enjoy!