Wow! Dredging up a nearly five year old thread. Welcome to the site, Richard. I'm sure many folks here and at the Parker Gun Collectors Association,
http://parkerguns.org/ would love to here more about your Parker and see some pictures.
Well, I've added a lot of long 20-gauge shells to my collection since this thread started --



So far Peters is the only company I've found to offer thier progressive burning powder loads in longer cases --

From the 1927 Peters Cartridge Co. catalogue --

The table of Widgeon Duck Club Parker Bros. 20-gauge guns on page 677 of
The Parker Story doesn't include serial number 159078? Those listed are 159075, 159076, 159077, 159090, 159092 and 159093 all ordered on April 22, 1912; and 163961 and 163962 ordered May 22, 1913. Well worn number 159093 is pictured on page 680.