If you can't do one bag, then carefully plan a second bag which you will leave at the hotel, along with your overcoat, in Korea while you take the single bag on to Burma.

Korea is more formal than Burma by far, so full suits similar to USA or Europe would be in order, long-sleeve shirts and winter weight. Regardless of nature of business.

Burma--a lot of business gets done in lightweight suits (like you'd use for summer in the USA), or in shirts and ties, no jackets. If you're selling or consulting, maybe veer towards the suits. If you're buying, then the other party will be more interested in your money than your clothes.

For either the casual business meetings or the casual sightseeing, take some khakis and short-sleeved or golf-type knit shirt for Burma. I learned some years ago that the most important person in the vicinity to be kowtowed-to is not the suit-uniformed guy, it's the fellow who looks like he's heading for the golf course. I think for Korea, a pullover sweater instead of the suit jacket would suffice for casual setups, and keep you warm (coat if outside).