I bought my car the way Stuart suggested. I had to increase the daily limit to cover the amount, but it worked with Bkk bank. Failing that, I think you can go into your bank and get some sort of payment mandate to cover the exact amount (apologies I don't know what it's called, it seems such an old fashioned method), but the bank will charge you for the service.
It is easy to do online, so why not try that about 8 days before the due date. If it is not approved within a week you can then go to the IO in person.
I have had no problems with the online system, but I know others have.
I managed to open one 2 years ago, but I am seeing a lot of posts saying that it has changed now. Definitely give it a try, ask the bank what they require first. You might need to try several banks before you find one that is willing.
I tried many banks and different branches before being successful at the Bangkok Bank.
The agent fee for this task seems to be about 4 to 5,000 Baht if you need to. Everything else with the visa process is simply providing the evidence requested by immigration and attending on the correct dates, so need for an agent for that.