Did I miss something or did the dialogue specify keeping the needle down when stopping to do another stretch?

An added thought - you could try posting this on Gatherings. Bill Holamn recently offered a reply as to a Europro machine. He has extensive knwoledge about sewing machines. Any of his insight would be on target.

Pattyv thought has merit. And as mentioned, putting on a machine & givingit a try might be helpful. I say "might" because the fork that attaches needs to be the proper alingment to the needle bar screw.
As to your other inquiry, I have presser feet I need to figure out for my mother's Singer industrial.

ETA - the foot is available on line from a variety of sources for interested members who require using this method.

This "movable" zipper foot is a must for every one to have at hand. Time was it came with the many feet included in a machine purchase.
With the arrival of snap on feet, it was replaced by a zipper foot that works but is limited.
If it matters to anyone, the movable ... is AKA narrow base ..., single toe ..., and probably others.
There's a generic foot on the market. If a sewists chooses to try it, make certain you establish the return policy before turning over the bucks. Last I saw it retails for $3.29 at JoAnn's under the Singer label, & is in the Notions aisle.
The needle bar on some machines is configured in such a manner, the machine needle will fall short of clearing the indent on the foot designed to accomodate it.