Can I do a border run from Phuket to Padang Besar and switch passports during the crossing?

You cannot change passports at a land border. If you go out via land border you must enter the next country with the same passport you stamped out of Thailand with. And the same rule applies when returning, so there is no opportunity to switch. It's only when entering via air that you can switch. You should also expect extra scrutiny and questions about why you are using a different passport than previously if you try it at an airport.