A criminal records check is only require for the non-OA visa. A 90-day non-O visa does not require any background check, health check, insurance, or any number of requirements that the non-OA visa requires. It's mostly just providing proof of funds.
You're not waiting 60 days. You're waiting 2 months. You cannot apply for the extension until your money has been in the bank for 2 full months. That means if your funds were deposited on November 8th, you cannot apply until January 8th.
If you have extra time, then go to immigration and ask them for their handout of requirements for the 1-year extension. That will allow you to make sure you have everything in order when the time comes.
First, I doubt you qualify for visa on arrival, which is where you pay for and apply for a visa at the airport and only available to a small number of countries.
Second, the fact that the embassy denied your visa should tell you something.
Third, one of the legal requirements for both a tourist visa and visa exempt is proof of onward travel leaving Thailand within 60 days. Even with an extension you can only get a maximum of 90 days and you probably won't even qualify for a 30 day extension. So a ticket out after 95 days is obviously a problem.