How to implement polymorphic associations in an existing database
You could use Option 1 but without an additional surrogate Alternate Key.
Instead, extend the existing Primary Key (of each entity), with an EntityType column (say CHAR(1), that would be E for Events, P for Persons, D for Products).
The compound (EntityId, EntityType) will become then the Primary Key of table Entity and the corresponding compounds in the other 3 subtype tables.
(The EntityType is just an auxilary, reference table, with 3 rows):
