GSP to MIA is $161, I looked at two different days and this was five segments. So that would mean 10 days of travel at a cost of $1610 if you could find this on 10 different days. If you are thinking about this, do more research and see how many segments you can buy today and what the cost is. $161 for five segments is exceptionally good, maybe $200 for four segments is more typical.

Going for miles would take two long trips, CGK is the best considering distance and price. For example, CLT-ORD-NRT-CGK-NRT-LAX-CLT is $1036 out 11/1 return 11/3, 21679 miles. This trip is available most days. After two of these you would need a short domestic trip, figure $200 at most. So this plan requires about $2275 and seven days of travel. You can do CGK from FLL for about $800, so if you wanted to position to FLL then do back to back CGK runs, you would have what you need for around $1800.

But ... since you don't have a passport this won't work. I think that going for segments is a better strategy because 45K miles would mean 9 or 10 cross-country trips and cost around $2500 best case - it seems like timewise it is about the same as segments and pricewise it is likely to be more.

https://www.google.com/flights/?f=0#...214;a=ONEWORLD
https://www.google.com/flights/?f=0#...=ONEWORLD;eo=e
https://www.google.com/flights/?f=0#...=ONEWORLD;eo=e