You could and can easily access Immigration in Chiang Rai, if you’re north of the river, you go to the Mai Sai office if you’re south of the river you go to the office in Central Plaza 
You missed my point, people might be tempted to overstay rather than try to get an extension. It's not a solution. Personally, I can't overstay for another 19+ years, I have 20 year Elite Superiority Extension
Excellent post Robert, the golden rule is choose the visa/method that is "appropriate" to your stay. If you want to stay here longer than the method you chose, you have already made one mistake. Don't make more mistakes. You must have the right visa, don't try and do it on multiple inappropriate visa/method. You will ultimately be denied entry and more.
You might get a one year permission to stay, but Thailand Elite will write to you to tell you that they have written to immigration and you will be overstaying. Whether you get away with it is another question.