Once used as non-inventory on an order, it can’t be switched to inventory in that site and vice-versa.  If you haven’t used it as the one, you can delete the information as non-inventory and re-create as inventory.  That is usually a narrow window however that has to be caught pretty early.

I understand this is how the standard business logic works.

However, I don’t find this to make much sense since sales people and customers shouldn’t care about whether an item is inventory controlled or not.

I am looking for someone who has successfully implemented a change process for this (probably including a job, RMB or similar calling and UPDATE statement on SALES_PART_TAB).

It can’t be converted, but there is the functionality - ‘the replacement part’ in Misc part info tab in non-inventory sales part if you want to make a connection between the non-inventory sales part and the new separately created inventory sales part.