I used a combination of the comments I got on the last post, some research on my own, and some hard thinking to make things far, far better.
I re-read the section on rabbet planes in Garrett Hack's "The Handplane Book" and checked out a few things on my plane. Hack noted that the iron should be slightly tapered in width so that it doesn't scrape the side of the rabbet as it gets deeper.
|Side tapered - check|
|It's about 1.537" wide at the business end ...|
|... and about 1.526" wide an inch back from the end|
|Wait ... what?|
|Are you kiddin' me?|
The first thing was to flatten the bottom of the leading edge and this was done quickly on a diamond stone.
|Almost done - a little more on the stone had this flat across the length|
|Leading edge after some filing and sanding|
The next thing I did was to make an auxiliary fence for the plane. Without the added wooden fence, the original fence is only about 1/2" tall. The new auxiliary fence is about 1" tall.
|Auxiliary fence added|
|Here's how I was holding with my left hand|
|A picture from above|
|First alternate grip|
|The grip that worked|
|View from right side|
|View from directly above - note there is no obstruction of the escapement|
|View from above and to the left|
|The victorious Record #778 rabbet plane and conquered shavings|