First of all, I would preface this by reminding you that you booked your honeymoon to SE Asia during rainy/monsoon season, so it's hard to have sympathy for you given the current circumstance.

Next, BKK won't ever shut down completely. It's one of SE Asia's biggest posts and too many carriers rely on it, so don't count on that happening.

Having traveled Cambodia, Vietnam, Thailand, Laos, Malaysia, and Indonesia extensively, there are many options ex-BKK that you could pursue to avoid the flood crisis in BKK. Beware that the rest of SE Asia is also presently overwhelmed by minor flooding and torrential rain.

Have a look at AirAsia and Jetstar Asia as well as Tiger Airways and Lion Air as LCCs who can get you out of this pickle. Given your budget, they will probably be your ticket. They're not part of any major alliances and you don't get to use any of your FF benefits, but their fleets are young, flights are short and they fly to all of the places you listed and they're cheap!

Also, be sure to check out Agoda.com for discount hotels in SE Asia. It's how my friend and I conquered our SE Asia travels staying in mid-tier "resorts" and never paying more than half the rack price. Plus, when you book on Agoda, things like breakfast are normally included in pricing which you'll find are not always included in your full price reservations.

Feel free to PM me if you'd like specific hotel/travel recommendations for Thailand or Cambodia.