Why wasting 350+ us$ into a visa while you can stay here for 90 days @1900baht for visa extension? If you want to stay here longer u can also apply for a multi entry tourist visa which can give you up to 9 months....
Up, the currency doesn't matter as soon as you have over 500k baht. You MUST apply in the country you are located, in your case apply at the Thai embassy of Rome bur prepare to show up the papers that prove you legally livein Italy