How can I change Referential Integrity from a Unique Key Constraint to a Primary Key?
There's currently no way to modify which unique index a foreign key constraint is "attached to" because this is supposed to be an internal implementation detail, the same way that a unique constraint uses a unique index behind the scenes to enforce the constraint.

In fact, as you saw, if you have multiple candidate indexes, the one the foreign key attaches to seems non-deterministic (it might go by index id, index width, or something else; I haven't played with it in-depth), and it cannot be specified in the DDL statement either (memory says there's a Connect item requesting that feature, though).

So in this case, at least for now, you'll need to drop both the foreign key and the existing unique constraint before re-establishing the relationship, to ensure your change script works correctly in all scenarios.