Seems like a funny question. You have 34,000 miles. You can get as close as 34,000 miles. But do keep in mind that the airlines' calculation of your mileage isn't necessarily the same as from other sources. Even Qantas, which purports to use Great Circle, will come up at a different mileage than if you put the same routing into the Great Circle Flight Mapper.

Tell the airline to put the routing into the computer and to give you a figure. That's their job. You have done as much as you can for the moment.

Incidentally, you can shave off about 500 miles by going to Berlin via Helsinki instead of London. Probably save you some taxes as well, especially if youre flying business class.

Also, you missed an impt rule. Your surface does count in the mileage. You actually have a routing that is 34,300 or so. But again, you can change the two segments and, with luck, be within the mileage amounts. I would feel comfortable with a 200 mile cushion but not a 13 mile cushion.