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

No you cannot, i tried that there many years ago they made me go back to Malaysia border and get stamped in with passport I left Thailand and then come back. Flying is only way to change passports and always found KL or Singapore the easiest.

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.