There is no written rule banks follow...you need to just go from branch-to-branch and ask a manager, do not speak with a pencil pusher. Many will require proof of address, which can be your condo lease agreement (minimum 1 year) or similar. Some will require a work permit....just keep asking until someone agrees to help you.
It is not unusual for frequent visitor to Thailand to have a local bank account. Foreigners are welcome to open bank accounts in Thailand on tourist visas.
All the visa company can do is go early and wait in line for you, but ultimately YOU must be there for the photo! We do not allow any visa agencies to be mentioned in this group as members can do everything themselves without the over-paid "paper pushers"...