To answer some of your questions, with renewals of a passport traditionally people just carry both passports.
I have seen other post with lost / missing / stolen passports and they were told to make a new application.
As the DTV is issued by ministry of foreign affairs (embassys) I don’t think immigration office will help you. Not saying impossible but with history of people trying to extend in country I’d imagine transferring the visa will be the same case.
Any way please share your feedback if you have any updates this will be a good one to follow 🙏🏽