If your 'zombies' are not truly undead, do they need the Undead Fortitude trait at all?
The zombies which appear in the Monster Manual are shambling corpses, bearing old wounds and rotting where they stand. Narratively, the Undead Fortitude trait represents a zombie simply not caring about a wound it received, because it doesn't need that organ you just impaled on your shortsword. A lucky zombie which passes multiple Undead Fortitude checks would have bits falling off and large chunks of flesh missing; injuries that would kill any living creature but aren't a big deal to zombies.
If your zombies aren't actually dead and can still be cured (I assume you mean by methods short of Raise Dead), then shrugging off organs being impaled and limbs being lopped off is far-fetched.
Consider removing the Undead Fortitude trait altogether for your zombies. If you feel this makes the zombies too weak, you can increase the hit points to compensate.
Since your zombies are disease-based, consider making this disease contagious, and thus give your zombies a trait more fitting to your campaign. Give them a Bite attack like that possessed by the Diseased Giant Rat (MM p.327, sidebar), except with your zombie disease instead of the giant rat's disease. If you fear that this might be too dangerous, you can make it so that the Bite attack can only be used on a creature grappled by the zombie, as for a Vampire. You could also make it so that the zombie can use its slam attack to grapple an opponent rather than deal damage (as a Vampire can). Since zombies don't have multiattack, this gives your players one round to try and break free from the zombie's grasp, which sounds like a dramatic moment which your players may remember for a while.
You could make the onset time for the disease sufficiently long that the party has enough time to race to discover a cure to save their ailing comrade, at your discretion. Even if the onset time is relatively short, the party could still try to cure their zombified friends. This may enrich your story opportunities. (Sample Diseases in DMG p.256)
Yakk provided a suggested stat-block for this Diseased Zombie (which I have extended slightly using the Zombie's regular attributes).
Str 13 (+1), Dex 6 (-2), Con 16 (+3), Int 3 (-4), Wis 6 (-2), Cha 5 (-3)
22 HP, 8 AC, Speed 20ft.
Multiattack: The zombie makes two Slam attacks. If both attacks hit a single Medium or smaller creature, the target is grappled.
Slam: Melee weapon attack. +3 to hit. Reach 5ft. One target. Hit: 1d4+1 bludgeoning damage.
Bite: Melee weapon attack. +3 to hit. Reach 5ft. One creature grappled by the zombie. Hit: 1d4+1 piercing damage, and the target must pass a DC 14 CON save or get Zombie Disease.
There are some variables which depend on the flavour and challenge you want these zombies to provide. You'll need to decide whether your zombies are undead type (making them vulnerable to effects like Turn Undead, Destroy Undead and Control Undead) or some other type, such as monstrosities or humanoids. You should also decide whether it is immune to poison damage and the poisoned condition like the normal zombie, and whether they have darkvision and proficiency on Wisdom saves (which presumably existed to provide some resistance to Turn Undead). You can also adjust the numbers as you see fit (I would have picked DC 13 for the Constitution save, because the save would probably be based on the Zombie's CON modifier, but considering the difficulty of getting a bite in a higher save might be appropriate).