While the keepers have some rare issues, i never had an animal starving so far.
I make work zones like you do most likely too, to manage the supply of mechanics and veterians and stuff.
But i keep the keepers in a special kind of working zone i sort as "Habitat I, II, III, IV" etc.
Each H-Zone has 2-4 habitats and as many keepers it needs, i monitor that careful and rather overstaff them.
A Working Zone can have several H-Zones and Vendors and stuff, but my H-Zones are small and easy to oversee.
I also have a very generous pathsystem for staff only. They have to cross a visitor way from time to time, but other than that they can move freely.
(That way i fked my zoo up in terms of transport rides, they will never work in the first zoo, but as long as the bugs are present i give a wet crap,
i want my furry little friends alive.)
The system with the working zone is great and, at least mostly, functional.
I use to suck at such things and am therefore overcareful, but i never, ever had a keeper working elswhere as i wanted him/her (not work at all, well yea).
Over 240 animals alive and kicking now.
Don't turn the time on fast forward, take your time in pause-function to check everything on a regular base.
Otherwise the franchise mode can be a little frustrating during the first time.
Now... i have to make it comfortable for my new lions i could finally afford... and the red pandas are matured and starting to fight... and my tiger breedings habitats are full...
and... oh is it that late again?...