What do you mean by don't trust minivans? This is the best solution for you to achieve your stated goal. Quick border bounce through agent will guarantee your next visa exempt entry of 60 days. Then you can extend it for 30 more.
You may want to consider getting the criminal conviction removed/expunged from your record. The waiting period prior to application will depend on your country.
You'll be fine, don't worry about it. If you need peace of mind, book a dummy ticket from an onward ticket website. For stamp extention you may need to wait until 45 or 30 days remaining instead of doing it immediately.
Not sure if "need" to. But probably should provide confirmation of business/tax registration. Most people report submitting it. But if you reply without it and the embassy wants it, they'll ask for further documents. Of course, this will extend the process.
As for other documents (not mentioned in your post), I would draft a cover letter briefly explaining your business, self-employed status, and remote nature of the work.
Regarding proof of location, you'll want to provide both entry/visa stamp and proof of accomodation (e.g. booking confirmation)