Change mailing address for automobile

I bought a Toyota Vios in Chiang Mai back in 2011, but I've since moved to Chonburi province.  I believe I'm obligated to change my mailing address of record with the Department of Land Transportation, but I don't see any reason to get new license plates for the car, unless it's required for some reason.

I went to the DLT near Pattaya, and I was told that I first need to get a Residence Certificate from the immigration folks in order to prove my new address, which I will do soon.  The existing stamp in my vehicle Blue Book indicates that my next road tax payment is due 5 days from now, on July 17th.  So I would like to take care of all of this in the next few days, but I'm not entirely sure of the process, and whether I will be in violation if I pay the road tax after that date.

I'm assuming I would do the following:

- get the Residence Certificate;

- take the Certificate to the DLT to change my mailing address of record.  I assume this will change my address written in the Blue Book;

- pay the road tax, which will be reflected in the modified Blue Book.

I'm wondering if anyone has already gone through this.  One of my concerns is whether any penalties will apply - I moved from Chiang Mai to Chonburi province about two years ago.

Thanks a lot in advance for any feedback on this!