There are a number of things there that are a matter of semantics and particulars. I'm not a rigger* and certainly wasn't in '71 (I started jumping in '79, and while piggyback rigs and square mains were by then prevalent for experienced jumpers, students still learned on the old 'gutter gear' type that was around in Cooper's day), so I'm not up on the different details of those rigs. My terminology is in differentiating between 'mains' meant for intentional jumps, which would require reserves and have the D-rings to attach them, and emergency rigs for pilots (or passengers/crew) who do not intend to jump but might have to. Hayden was not a jumper, but was an aerobatic pilot and therefore was required to wear one while doing that type of flying. Those rigs are reserves, which use reserve type canopies and must be packed and maintained by a rigger.
"Pioneer/Steinthal" - Pioneer was a company unto itself and I believe at times made both containers and canopies. Steinthal was a different manufacturer, and I could be mistaken, but the way I remember reading those documents, it sounded like they made that 'second' canopy, which was an 'integral' part of the system, that I can only conclude was the pilot chute (and the 24' rather than 24" was likely a typo).
I personally would want a steerable canopy, because that could make the difference between indeed landing in trees versus an open field next to them. A reserve type canopy that had steerability would likely only have about 2-4 mph to work with, while a sport main of that era would have maybe 6-12 or so. Depends on the type and the weight of the jumper hanging under it.
Any of the reserve canopies, including the 26' conical, might have no steerability, or it might have minimal drive slots, or it might have a 4-line release. My first reserve ride was also on a 26' Navy conical, and it had drive slots. That thing was 4 years older than I was! Was packed in an early piggyback rig.
*They don't just bestow rigger or instructor ratings on people at certain levels of experience. Ratings are things you take courses for if you're interested in the job. I was never interested in packing reserves or sewing repairs, so I never went for a rigger's rating.
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Has anyone asked the museum recently about checking out that rig? The rigger I referred Shutter to is the same rigger who he and his son did the re-creation jump in that last TV show you appeared in. He has all the creds the museum would need to be comfortable with letting him handle it.