The reasoning behind the long run extending by 1.5 miles every two weeks is that it allows you to build up your endurance beyond what you previously ran while also helping minimize injury risk. The shorter runs during the week are "maintenance" runs. They allow you to keep maintain your most recent long distance.
So while it may be possible to cap at 6 miles and still finish on race day, that may not equate to a more enjoyable experience come race day itself. You will be much better prepared and probably enjoy race day substantially more if you have run closer to the actual race distance in the weeks leading up to race day. In 2011 and 2012, I slacked off on the weekend runs for about 6 weeks. In order to get the distance in, I had to cut the short weekend runs out altogether and increase each long run by 1.5 miles every week to get the long runs in a still have a taper period. This worked, though I enjoy running a lot more if I have a "short" run built in.
If you were to run long runs of 7.5 miles on the 18th, 9 miles on the 25th, 10.5 miles on the 1st, and 12 miles on the 9th, you would be right on target for 13.1 miles come race day. While this may not be ideal, it's probably a better option than sticking with 6 miles and hoping it's good enough. In my experience, at least part of the benefit from the long runs is learning to push through when you're tired and being better prepared for the distance itself.
Again, each runner is different so what I outlined may not work for another, but I firmly believe that you will feel much better about successfully finishing if you have already come at least close to the required distance and will probably enjoy the whole experience more if you are better prepared.