PrecisionAir will book your luggage through to London from Zanzibar if you ask. Once you arrive in Nairobi you go through the transfer gates and walk for what seems for ages through the terminal to the Turkair lounge where they will let you in (1st/Business and other eligible pax) with either a boarding pass or by using the app.
The numbering of the gates in the new terminal isn't particularly obvious when you arrive in the "new" terminal but go past gate 4 before passing a luggage shop and the prayer rooms and the lounge is on the left. It does get busy but arriving from the 1830 PrecisionAir flight gets you there when there is still plenty of time to get yourselves some seats. It must be easy, we have done it lots of times since the lounge opened a year or so ago.
Leaving the airside areas with a four hour wait sounds attractive at first consideration but by the time you have gone through the formalities that time is significantly eroded. To leave the airport brings in more security checks at the airport exit/entry and you have to go through the Nairobi traffic. Boarding is usually quite early and the time soon goes.much, much better than it used to be both before and after the