The reason for the blackout on those dates is that the weekend of the 28th of September to the 3rd of October is Korean thanksgiving or Chuseok and is the busiest travel season of the year. Korail regulates sale of these tickets in batches (some going on sale 2pm Korean time tomorrow 5 September Wednesday) but it is generally almost impossible to get tickets for the weekend. You will have to be very flexible on times and days you want to travel and even then it will be a push. As for flying, most people have booked flights months ago (I booked in April) because flights are ridiculously expensive and full during this weekend too. Try tomorrow, otherwise I would suggest trying to change your plans or consider taking the bus. (Although if you take the bus, note the change of travel time from the normal 2 hours up to about 6 hours given the unbelievable amount of traffic on the roads.) The bus websites are generally in Korean unfortunately. Here is the website if you want:
https://www.hticket.co.kr/main.action Hope this helps...