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Here is a possibility: Assume the natural position on the left can be reached. White doubles, Blue takes, and White rolls 11, breaking her 6pt. Black rolls natural point-making numbers without using 6pt builders and breaks her midpoint, while White rolls four consecutive 41s, stacking eight checkers onto the 8pt. Black runs off the 18pt with boxes, which should get another couple checkers onto the 6pt. Finally, Black runs one checker from the 21pt while White meanwhile has been rolling four consecutive 53s. Black rolls 55, running his last checker, exactly putting an eighth checker on the 6pt and bearing off a checker. White then rolls a bunch of 42s (maybe 22 or 44 once, whatever it takes to force fifteen to the 1pt), while Blue bears off seven checkers and leaves eight on his 6pt. White rolls and comes down to four on her 3pt and eleven on her 1pt. Black isn't strong enough to redouble; he rolls boxes, White rolls 22, and now Black is suddenly too good to redouble.
Nack