Welcome to FT.

First, I would suggest removing your credit card score from your post. No one here needs to know that kind of personal information.

Second: Your trip is likely to be difficult to schedule, partly because you wish to travel to two quite different regions of the world, and partly because the dates you're looking for are in a busy period for holiday travel. Your first step is to see what airlines offer flights between El Paso and Iceland, and what airlines offer flights from Iceland and Bangkok. Then determine what alliance or alliances these airlines belong to. Your best bet will probably be to seek one or more credit cards with the chief USA airline that participates in the same alliance.

AA and UA offer one-way award flights at half the mileage of a roundtrip; DL and US do not do so, although DL plans to begin doing so in 2015. You may wish to try to draw on more than one program to book your flights.