Do you pay for your own travel (+ reimbursement?) or company-paid? What sort of annual spend is involved for this pattern?

I know I'm a bit of a broken record on this (a metaphor possibly lost on anyone younger than 50) but have you considered a round-the-world ticket? These have different prices depending on the country from which travel begins, and at present a business class Star Alliance RTW good for up to 29,000 flown miles has a base price ex-Japan of $4355. (The same ticket with travel beginning and ending in the USA has a base price of $10,426.) With that ticket you could fly a route something like this - or any one of thousands of variations.

If you were willing to switch to Oneworld program (which might be better as it includes Alaska as well as Japan AL, Cathay Pacific Malaysian, and Sri Lankan) you could use a Oneworld RTW that has no mileage limit. See the recent posts on this thread - Round the World - Star Alliance - $3k-$4k Ex-Italy - Page 3 - FlyerTalk Forums for a little additional information. Just a thought, anyway.