The price is mainly determined by two things: the starting location, and how many miles you fly.

There are three miles thresholds that are used for pricing 29.000, 34.000 and 39.000 miles. That's where the difference in your prices seems to come from (they price at about $16.000/19.500/23.000 for 1 person in F when starting from the US).

And it really seems unwise if you look at the cost not to start from NRT since that's where you are ending your route anyway and flights there are plentiful.

Also the schedule you have posted hardly seems worthy of an RTW ticket. Two returns with a stopover could accomplish the same and be a lot cheaper. The RTW tickets have a few selling points, their flexibility (you can change the dates without costs, and the routing for very little) and the ability to get you to the smaller airports or off the major routes for a decent fare. If you just fly to the major gateways then there are often options that cost less. And since the aim is to fly F in the best cabins, you're probably looking at major hubs.

You could also look at the SQ RTW options, just on SQ metal and no flights between JFK/LAX but it might be cost efficient.

Also something to keep in mind.... an RTW in F will earn a decent amount of miles, so you might get an additional free ticket out of it.