Unable to change POS Profile with a bad "series" value

I have an issue with POS Profiles. My existing global POS Profile has no series. It is just listed as “select”. This also means that sales invoices created through the POS have “select” in their name - which is far from ideal.

To try and correct this, I want to change the “series” field, but I cannot since the field is read only. I then tried to delete the profile, but I cannot since it is connected with sales orders.

no delete

Finally, I tried to create a second POS Profile, but then I get an error about there already being a global profile.

How can I fix this issue? How can I edit the “series” field? Or at least, how can I delete this profile and create a new one with a valid “series” field?