So I can answer my own question. . .
I checked inventory again for the flight I was most interested in and again found two seats available for upgrade of economy tickets to Prestige business class. So I called Korean Air.
The agent said there were indeed two seats available for upgrade so she processed the purchase of the ticket and transferred me to the "ticketing department" to process the upgrade. 45 minutes start-to-finish and it was done and ticketed in Prestige business class.
She told me I could purchase the ticket online and then call back to have the upgrade processed, but I decided that given what I went through yesterday, it was worth the $30 phone processing fee to just have it handled before I hung up the phone.
Still no idea why I was unable to get this done online. The online system seems to be in place to do it, as the prompts throughout the process clearly indicated, but in my three attempts, each time after ticket purchase it told me seats were no longer available for upgrade. In the future, I'd be pretty confident in booking an economy ticket that's eligible for upgrade if the system tells me the upgrade is available, then call in to process that portion of it. There's not much risk, as I have 24 hours to cancel the ticket without penalty. As I did three times yesterday.
Note: If you do this, be sure to go through the process on the website to check inventory for "economy upgrade to Prestige class" seats, as this will give you the upgradable fare that you need to purchase. You may get lucky and the system works as intended and processes the upgrade right after the ticket purchase. But if not, just call in to have an agent process it for you.
For the KE experts here, any thoughts on this? Does it usually work online? Or should one just plan to just check inventory, book the upgradable economy ticket online and call in to process the upgrade?