A lot of uncertainty here given the details. Programs could change/devalue since you are looking quite far out, and there is a big difference between Japan and New Zealand as destinations for example. Also saying you'd like business for long flights is a little vague. What is long to you? Is business absolutely required? I assume you all need to be flying together but that’s an important detail as well, because looking at space for 4 is different than 1 or 2. You might get better responses if you propose five or six specific routes that you are looking at in your itinerary.

Southwest points can get you to Costa Rica from IND, but it won't be much help with the rest of your plans. I’m not sure what an average fare is for this route, but if the point is having enough miles to not pay cash for flights on this trip, I wouldn’t be trying to accumulate too many Southwest points. But if you plan on flying back to the USA after this before going elsewhere and want to fly Southwest, then applying for a Southwest card could be useful.

AA plus partners has great coverage for South America, so using those AA miles for that part of your trip could be a good use.There are redemption's USA-Asia for 32,500 AA miles in economy. 60,000 miles business USA-Japan or 70,000 miles to other non region 1 Asia destinations. Finding multiple business seats probably would be tough. Multiple AA cards through Citi and Barclays give some options for accumulating miles.

Alaska Air does have great redemptions on Cathay Pacific, and you could potentially do USA - Hong Kong (Stopover) - New Zealand for 60,000 miles one way in business. But getting enough miles and finding space for 2 people (let alone 4), wouldn't make it a realistic option. And you can’t transfer UR or TYP to Alaska Air.

British Airways is good for non stop economy flights on various partners (miles cost is per leg and based on distance), although a few more miles now than before. I like these miles because of the generous cancellation policy too. They are a transfer partner of Ultimate Rewards, and through June 16 there is a 30% bonus on transfers, so its 1 to 1.3 ratio. I could definitely see them being useful on intra-europe or intra-asia flights, especially if you aren’t wanting to fly cheap LLC’s around.

Maybe someone else can chime in on tips with Star Alliance airlines. Most of my knowledge is with Oneworld. I do know that Singapore Air is transfer partners with both Chase UR and TYP, so you could potentially have a lot of those miles.

Another potential card to apply for is the Barclaycard Arrival Plus World Elite Mastercard. It’s never gone above the current 70k offer, and it basically would give you $700 in travel credit to use toward airfare or other travel costs. It’s nice having a straight travel credit available, giving you some flexibility to reimburse a cash airfare rather than only being able to use miles.

Hiring a service is one option but if you want to DIY, I’d recommend playing around with the FlyerMiler website on different routes. I’m not sure if its super up to date with recent award chart changes (I’ve seen some inaccuracies on there), but it will help at least give you a better general idea where to start.