Well Dave it seems that you have solved your problem. But just in case I thought I might add a few ideas:

1. If this plane has an adjustable mouth, try closing down the mouth opening to get a really fine shaving.

2. You might try taking a piece of of scrap say 24 inches long, 1.5 to 2 inches wide, and about 3/4 inch thick. Using a table saw cut a shallow dado about 1/8 to 1/4 inch deep lengthwise on the wider face of this board. Make the dado just wide enough to push the pieces that you are planing into the slot, this will hold your strip on three sides while you work on the fourth edge.

As for your Christmas list, look at the Veritas low angle apron plane (0P527.02), it is excellent for fine work like tapering strips.

Just my opinions.

Greg