Just to add to Tod's response, you must be back in Thailand in time to apply for your next extension, so don't leave it until the week your current extension expires (apologies if this is obvious).
Really depends on the Amphur you are dealing with. Some people seem to walk in with a note on the back of a fag packet and walk out 15 minutes later with yellow book and pink id. It took me weeks, lots of running around, several visits to the Amphur, Embassy letters and documents from Ministry of Foreign Affairs. I already had the documents from the land office including usefruct, showing I own the house etc. It's much more difficult than the visa process in my experience. Good luck.
You pretty much answered it Harry, take your rental agreement and non-O visa in your passport to immigration and tell them you need the letter to open a bank account. I think an immigration office in Bangkok is reluctant to do this, but the vast majority in Thailand will issue it without a problem.
Opening a bank account should be possible without an agent, provided you come to Thailand with a non-O 90 day visa. Some banks seem reluctant to open accounts for foreigners, but it's a case of trying several banks until one says okay. You will need a Thai phone number and a letter from immigration confirming residency.
If you pay 65,000 baht into your thai account each month of your first extension, you can use that for your second extension and withdraw the 800,000 baht immediately after.
Get the non O 90 day visa online from the Thai Embassy before travelling to Thailand is the simplest way. You can then open a bank account in Thailand and extend your stay by 12 months annually.
It used to be possible to open a bank account in Thailand without a long term visa until this year, when the banks were scrutinised and stopped. He therefore needs to travel to one of the neighbouring countries ((Vietnam, Laos etc), apply online for a 90 day non-O visa and once granted, return to Thailand, open a bank account to start the process.