If you decide the agent route, I recommend Lawyers for Expats (Thailand) - Brian Ramsden and his business colleague, Mint. They are also open to an initial "free of charge" consultation.
Banks have certainly tightened up on who they grant accounts to and staff are bound to following refreshed account opening guidelines. Having said this, and from experience, there are variations from one bank to another, one branch to another, and one member of bank staff to another on how they apply the refreshed rules. Some documents seem to have become mandatory though: Passport, Visa Certificate, Certificate of Residence (to obtain this from a local immigration office needs: Passport, 2 x Passport Photos, Proof of Residence - (Rental Agreement), Copy of Visa, Complete a Form, Pay 500THB). If you are unable to provide all of these documents due to your circumstances, try to visit a local immigration office and explain your situation.
Applicants have a choice whether to use a visa-agent or not. This Agent's fees are not a scam, it is their charging structure and covers staffing, overheads, knowhow in advising on and uploading documents etc. Applicants who are digitally savvy can do it themselves.
Dirk Scheffenbichler, yes. I have been through the Malaysia - Thai border several times in recent months, and witnessed the questioning. If I am not mistaken, you are allowed 2 border crossings per year on visa exempt and/or tourist visa
Passport, Proof of Residence (rental agreement if renting), Visa Certificate (show original initially), 4 x PP colour photos (or have them done at immigration if they have a facility), complete their form and pay 500THB per COR purpose ie. You need separate ones for bank, car and motorbike driving license applications.