Okay, here we go.
Trigger1 ON, NOT LOOPING
Condition1: Object has target (your zombie)
Condiiton2: Bring object to object (your zombie to another unit)
Condition3: Bring object to object (the other unit to your zombie, yes it works better this way)
Effect1: Activate trigger2
Effect2: Activate trigger3
Trigger2 OFF, NOT LOOPING
Condition1: Object has target (your zombie)
Condiiton2: Bring object to object (your zombie to another unit)
Condition3: Bring object to object (the other unit to your zombie)
Condition4: Timer 3
Effect1: Deactivate trigger3
Effect2: Change ownership (the other unit to the zombie's team)
Trigger3 OFF, NOT LOOPING
Condition1: Timer 4
Effect1: Deactivate trigger2
Effect2: Activate trigger1
That should work, but you'll need to do that for every unit that can convert, also those units won't be able to convert on their own. I could if you like make you a data file that works more convincingly, but you'd have to include that with the scenario.