Wow, Bali sounds great and it's not unreasonable to collect all the miles in 6 months. This is actually a really good challenge, but completely doable. I personally would go for Star Alliance as they have by far the best availability and some good opportunities to get points quickly. United charges 65k miles ORD-Bali so you'd need 325k miles for all 5 tickets.

1. There is a semi targetted offer for 55k UA miles right now. Go to the UA forum to read up on that.

2. Chase Sapphire Preferred offers 40k miles signup bonus,

3. Chase Ink Bold Business card offers 50k miles signup bonus.

Ideally, if you can get the targetted offers, you should be able to each get the UA card and Chase Ink Bold on the first application. Then 60 days later, get the Chase Sapphire Preferred. The signup bonuses alone will give you 290k points. If you already have some miles and can manufacture some spending, getting to 325k points is doable.

The plan is very aggressive, but not impossible. Of course, only you can decide whether this is the right plan for you and your finances. I am just providing a best case scenario!