I think the most important question is, why did you wait until 15 days before your trip to ask about this???
So without any visa, you will arrive "visa exempt" which is not a tourist visa. It means you have NO visa, and will be stamped in for 30 days which you can extend for another 30 at an immigration office.
As you said, after that you would need to do a visa run or border run. If you leave and re-enter with or without a visa, you still won't have enough time to cover your entire 6 months, since you'd get either 60 more days or 90 more days.
The best thing to do is to apply for a visa before you leave.
Will you have enough time? I don't know. Each consulate has different processing times, so I can't tell you how long yours will take. Now that everything is done online, it's faster than it used to be though.
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You would apply at this website. You can either apply for a single entry tourist visa which will get you stamped in for 60 days, which you can extend for another 30 days, or you can apply for a multi-entry tourist visa, which is valid for 6 months. This means you can enter Thailand an unlimited number of times in 6 months, and each time you enter you will be stamped in for 60 days which you can extend for another 30 days.
With the single entry TR, you would need to go to a neighboring country after your first 90 days and apply for a new tourist visa at the consulate in this neighboring country. Expect a trip of ~3 days, depending on the country/consulate you choose. Once you have this new TR you can then re-enter Thailand and get another 60+30 days, giving you your 6 months.
If you get the Multi Entry (METV) you would spend your first 60+30 in Thailand, and then exit the country, stamp into another country, and then re-enter Thailand and get your next 60+30. Note that some land borders require you to stay in the country for at least 1 day (I believe some of the borders in Cambodia have this requirement). The benefit here is you don't have to go to any consulate and apply for another visa, you just jump out and jump back in.
Note that the METV is more expensive than the TR, but you would save money on spending time in another country. Which option you decide is up to you.
If you don't get a visa, you'll have to leave Thailand and re-enter 2 times during your trip, and you may be questioned about why you are leaving and re-entering so much when you don't have a visa.
As a final note, your airline likely will not let you board your flight to Thailand if you cannot show proof of onward travel (proof that you will leave Thailand) within 30 days if you are entering visa exempt, or 60 days if you have a tourist visa. To get past this you may be able to show a cheap bus or train ticket out of Thailand within that time, or a cheap flight to Vietnam or Singapore. You can also google "onward travel ticket" for other options.