A bit of a novice when it comes to all things BAEC and tiers. Out of traveling for work, I've managed to gain Bronze, and new tier points year just reset so I'm back at zero.

I was wondering what would be the best way to maximise tier point earning, and at an OK price for a trip over July / August this year. I need to do a visa run - so would need to go London - New Zealand, stay for 3-4 weeks, then tack on a trip to Taipei for a week, then back to London. Realize that Taipei is a bit out of the way and not a standard stopover like Singapore or Hong Kong - but hoping I could swing it? I wouldn't mind stopping by Singapore for a couple of days if that helps?
Is it worth getting a One World RTW ticket for this type of trip? I think I would need to fly in the same direction so might need to go something like London - USA (NY / Chicago / LA) - NZ - Taipei - London?

[Secondary question] Also I think it is more worth flying with One World, but a little part of me wants to try and hit KrisFlyer Gold as I signed up to Infinite Journeys and if I complete 3 trips via Singapore Airlines I could get Star Alliance Gold. But, seeing as I'm based out of London, I'm thinking One World status might be better. Does anyone have any experience with this accelerated earn, and how quickly it gets awarded (ideally I could use it for the Koru lounges in New Zealand?).