They always slip a new one into my passport in Chiang Mai. I just did my extension a few weeks ago and when I asked she showed me it tucked into the plastic cover for my Passport.
I was doing exactly the same 6 and 7 years ago so I believe the only thing that has change is the appointment system now whereas before you just rocked up and hoped the queue wasn't too long.
You need a TM30. Where are you staying in Pai? Ask at your lodgings/hotel for a copy of the TM30 they should have filed as it's their responsibility to register any staying guests.
Your current visa exempt stamp is void as soon as you stamp out through immigration regardless how many days are left on it but you can easily get a new visa exempt stamp when you come back to Thailand.
