I would second this suggestion. It has been reported as having worked for others in the past. That is, UA can open award C or F seats for you on its own flights. Be persistent and you might have success in having someone do this for you.
I'd third this suggestion. And if you can secure a satisfactory change, (calmly) fight like hell to avoid having to pay UA change fees for a situation that was way beyond your control. A few other thoughts:
1. First, this is truly a lousy development for your honeymoon. You have my sympathies. But don't let your (and your wife's) understandable anger leak into your dealings with UA. Be firm but calm in talking with the airline and escalating the matter to a supervisor. And certainly play the honeymoon card in trying to get someone who'll make an extra effort for you.
2. Check everyday with UA to see if alternative C routes on UA or other *A flights have opened up that would get you to BKK to make your connection or that might get you most or all of the way to KCH without going through BKK. (OZ from ICN to BBK, for instance; or ANA/UA via NRT to BKK; or with some real luck flying wonderful SQ all or part of the way to KUL--though be aware that with a C award ticket SQ's policy is that the short SIN-KUL hop might be in Y). This can certainly happen as you get closer to the departure date, plus the lousy political developments and airport closings in BKK could work in your favor in terms of some folks canceling their award trips. Find out what all of those alternative routings are, so you can suggest them to the UA CSR, who may not know to look for them.
3. If worse comes to worst, take the flight in C the next day, eat the costs involved in the other changes, book a room at the airport hotel in Inchon (which isn't anything special, but as airport hotels go is fine and well-heated) so that you don't have to venture outside in the dead of winter, enjoy the weirdness of spending 12 hours or more in an international airport (and as international airports go ICN isn't bad), and try your best to laugh it off. Stuff happens in marriage and life--heck, we were in a bad car accident near the start of our honeymoon but fortunately escaped with just a wrecked car rather than wrecked bodies and went on to have a wonderful trip (and marriage!). I know I'm comparing apples and oranges here and that eating the costs might be easier for me to say than for you to do, and again I agree that this is an aggravating situation, but it's better to just move on at some point rather than to remain angry and let it ruin what will be an otherwise great trip.
4. The one thing I'd recommend not doing is accepting a long-haul flight in Y, at least not on your honeymoon.
5. I doubt that it would work, but maybe if you have to cancel your Air Asia flight from BKK under one of the above scenarios you could say you've done so because of the airport closures and the possibility of future ones, and therefore press for a full refund.
6. If you do get UA to do the right thing and make the changes for you, get the name and location of whatever employee does it, so you'll have that info if something else messes up with your reservation.
I hope things work out well, one way or the other.
And congratulations on your marriage!