Rabbit:
My comiseration. The Parker is one of my leading candidates for the "Rube Goldberg Award" of double gun designs ever invented. And NO, you can't get the buttstock off an undamaged Parker without FIRST removing the sears. Mr. Wood must have been smoking something powerful when he did that section -- or just horsed the stocks off like most American 'smiths.
Nonetheless, experience is still the best teacher. For an accurate take-down sequence check the lamented Double Gun Classics online mag. Printed versions are available from Cornell Publications.
Best, Kensal