[SalesForce] How to change existing managed package field to unique

As per the SFDC ISV packaging guide you cannot update the page layouts .The page layouts are not up-gradable and hence only way you can launch new layout is create another page layout and probably deprecate the older one .

I would pretty much entirely dismiss

1. Constants in apex class: It's not possible for the end-users to modify them; they're not good practice anyway)
2. Custom objects: Can't ship them, end-users can't deploy them. You're wanting to store metadata and the platform intends you to use Custom Settings or Custom Metadata for that
3. (a) List Custom Settings - These days, Custom Metadata is better in almost every way

Which leaves you with

3. (b) Hierarchy Custom Setting - Useful because they are per-user, and for storing lots of different settings together. Bad because you can't package the values, and the end-user can't deploy them
4. Custom Metadata - the best option if you can make it work. You can package the values, and end-users can deploy them.

The downside of Custom Metadata is that you have to use the Metadata.DeployContainer and similar classes to write to them from Apex and this has to be done asynchronously. Nevertheless, you can write a Visualforce page, or Lightning Component to make this relatively easy for your end-users.

See https://developer.salesforce.com/docs/atlas.en-us.apexcode.meta/apexcode/apex_class_Metadata_CustomMetadata.htm for details.