Longtime reader, but this is my first time posting. My girlfriend and I have been talking about a RTW trip for a while now and are tentatively thinking about planning one in 1.5-2 years. I currently have the following points (hers in parenthesis):

American Express: ~300k
Chase UR: ~65k (~50k)
Delta: ~145k (~50k)
AA: ~180k (~50k)

We want to do something along the lines of NYC > CPT > BKK > NAN > SYD > AKL > LAX/SFO. We are hoping to use miles to book the entire trip, and are trying to figure out if it's best to save up and book a RTW ticket on points or book individual flights with points on different airlines.

We are obviously in the embryonic stages of planning, but any help and guidance would be greatly appreciated. Thanks in advance.