It's VERY risky to leave Thailand if you have an education visa from a language school. Because this is the most abused visa in Thailand currently, anyone with one in their passport is almost sure to be pulled out of line at the airport and questioned. It basically comes down to this: You applied for an education visa because you NEEDED to be in Thailand to study, and you NEEDED a visa to stay to do that. Therefore you should be in Thailand studying because you needed to be there so badly that you applied for the visa. As far as the immigration officers are concerned, if you left Thailand then you didn't need to be in Thailand so badly, and you didn't need to study so badly, so you lied about originally needing a visa.
If you MUST leave Thailand, then you should get proof of why you HAD to leave, get a letter from your school stating that they know you are leaving, why you are leaving, and that you are approved to leave and when you will be returning. This letter should also include the direct contact information for the administrator of your school, that way the immigration officers at the airport can call them if they want to.
2-3 months ago there was someone who had all of the above items, and the immigration officers did call and speak to the administrator, and then they were still denied entry to Thailand and forced to fly out.
So you spend 180 days in Thailand. Get an extension and spend 2 months of that extension. You're now at 8 months in Thailand. the EARLIEST you can get the next extension would be 6 months from that if you have to leave for some reason and return. Which means it's impossible to get another extension in the same year. There are only 12 months in a year and the earliest your scenario would want another extension is month 14.
You can extend only one time each entry. The reason they say once per year is because there are only 365 days in a year. How would you apply twice after 180+180 days?
METV can get about 9 months in Thailand. Each time you enter Thailand you can get a 60 day entry stamp and a 30 day extension. You can do this 2 times then just before the visa expires you can do it one last time and get another 3 months for after the visa is done.
That's 60+30, 60+25ish, 60+30.
If you only need 6 months that should be plenty, but as you stated you will need to do at least one border bounce. They run about 3-4,000 baht if you use a land border bounce agency to drive you there and back. Or if you can find a cheap plane ticket to somewhere that doesn't charge your nationality for visa on arrival, you might be able to do it cheaper yourself.
A DTV would get you a flat 180 day entry stamp on each entry and it costs 10,000 baht.
That's between you and the bank. But most people have reported that the banks will not give any special preferences to a DTV holder as it's just a tourist visa. You'll likely need to use an agent to help you open one.