You're not allowed to change lane once you've entered this type of roundabout. In practice the lanes are separated by a curb. Of course you still can change lane at the points where traffic joins the roundabout, but it's a sharp 90 degree turn and you'll discover real soon that it's a mistake to try.
I assume that traffic on the loops always has the right of way over traffic trying to enter the loops?
In that case, why can't you keep going around? At the place where the northbound inner loop becomes the southbound outer loop, it crosses the start of the southbound inner loop. The cars coming from the south trying to enter the southbound inner loop have to yield to the cars on the northbound loop, so it should be perfect safe for those cars to turn onto the southbound inner loop.
Note that allowing this maneuver is necessary if you want to allow eastbound or westbound travelers to make U-turns. If it is not allowed, then only northbound or southbound travelers can make a U-turn on this.