I made "custom" mobs by adding player_heads with curse of binding to mobs. These mobs will replace the player_head with even a leather_helmet if it encounters one... breaking the illusion it is a custom mob.

How to reproduce

/summon husk ~ ~ ~ {CanPickUpLoot:1b,ArmorItems:[{},{},{},{id:leather_helmet,Count:1b,tag:{Enchantments:[{id:"minecraft:binding_curse",lvl:1s}]}}]}

/summon husk ~ ~ ~ {CanPickUpLoot:1b,ArmorItems:[{},{},{},{id:player_head,Count:1b,tag:{Enchantments:[{id:"minecraft:binding_curse",lvl:1s}]}}]}

Throw a diamond helmet at both husks; the second one will pick it up, replacing its item.