We came through Korea last year.
Deal as a tourist is . . . . . . . .
90 days maximum entry for you and vehicle.
Need to pay 'deposit' to ensure vehicle exits country. (this is based on replacement NEW value of vehicle, but it is negotiable, they wanted $2000 from us we settled at $1000. This was fully refunded upon exit)
You need to purchase Korean insurance at point of entry, cost based upon vehicle, we had to pay approximately $100 per month (expensive!).
Carnet is not recognised in South Korea.
A very ( VERY ) good contact is Wendy Choi, she works for the shipping agent we used, speaks excellent English, very nice lady, friendly and ever helpful in any way. Good (and low price) shipping agent.
I am sure if you contact Wendy, tell her you a friend of Philip & Angela she will make further enquiries for you and help if she can.
her personal email is : WendyChoi2 'at' Gmail.com
Korea is an easy country to get extended visits to, I do not think you will have a problem for that. But, they do not get many tourist vehicles and so that maybe more difficult to arrange and probably expensive.
Perhaps, store on sell bike and just buy another in Korea for the duration of your stay??? may work out cheaper.