To give some idea of the total cost I have booked the following in the past three months (both are 16 segment DONE4s in USD):
Ex-TYO $5,798 + $1,197 = $6,995
Ex-KEF $6,207 + $501 = $6,708
The base fare for TYO is now quite a bit lower. I don't have the full breakdown, but I assume that the taxes and fees are much higher on the ex-TYO routing because there are more BA segments. (BTW, you can get in and out of KEF on AY).