@John *******
that's a stay over 3 months. You can get a 60-days "admitted stay" stamped when you enter visa-exempt. And buy a 30-days extension on Immigration for 1900 THB. It would carry you until February 2nd. It is unclear if you will be allowed another visa-exempt entry so shortly after having had one plus having maximized it. I instead recommend you leave Thailand before the first 60 days are expired, stay in a neighbour country for a 1-2 weeks holiday, then re-enter visa-exempt and get stamped in for another 60 days, which would show that you are a typical ("real") South East Asia tourist. Your chances of being allowed entry again are 100%