Been so long since I stripped the car I can't remember ...

My new headliner is one piece but I have the cardboard pieces as well as the toothed pieces for the sail panels. Wondering if the headliner gets cut and the material gets attached to the cardboard for install.

My initial thought is that the cardboard pieces are screwed in palce and the headliner gets installed in one piece.

There were 2 types: with separate cardboard sail panels that went over the headliner and were covered, and full headliner without the cardboard panels.
Was either a labor-cost or materials-cost deal, seems to me.
Reproductions may likely handle either style.

I'll look at my '68 & '69 when I get a chance, and post a comment.

I've never installed a headliner in a car before, and am in the middle of it.

As said they came two different ways and I don't know if anyone ever figured out which plant did what, at what timeframe.

Mine was built with the separate cardboard sail panels that had material wrapped around the cardboard, and my replacement headliner is the shorter style that has to
install like mine originally was. I'm okay with that so it looks like I'm restoring it by default. According to the experts mine is a September 68 Lynch Road build.

There is a weird looking clip that appears to, most likely, been glued to the cardboard and then shoved into a hole in the Sheetmetal. I can get a pic of the funky clip if you can hang on for a bit.
Whatever was holding the clip/assumed to be glue to the cardboard failed when I removed the warped pieces, so the clips are still stuck in my inner C pillar structure.
Looking at it, I'm considering 3M dual lock or similar instead of the glue.

If yours originally had the tack strip with the teeth mounted in the middle of the C pillar, it more than likely had the same arrangement as mine.
But you can improve on it, and regardless of how it originally came, if your headliner is the longer style then you can delete the separate wrap around the cardboard and
achieve a cleaner look.

i have done several headliners, including the one in my charger, which i did in naugahyde instead of the original cloth.
i also did the headliners in my 1947 plymouth sedan and my 1938 plymouth coupe, both of which were also naugahyde instead of the original cloth material.
they weren't particularly difficult to do, just time consuming getting them installed and stretched taunt, removing any wrinkles.
i did my charger and plymouth sedan with the windshields and back windows in place. the plymouth coupe had the windshield, back window, and the quarter windows removed for replacement at the time, so i installed the headliner in it when the glass was out.
a small heat gun helped eliminate the wrinkles, and i used several blunt plastic "spoons" to tuck the material into position. some of these tools were home made, just to get into some difficult places the other "spoons" couldn't reach, or were the wrong shape needed.
i also did a one piece headliner in a 1973 dart sport a couple of years ago. i will NEVER do another one of those !
the only thing available for those cars and others that require a one piece headliner, are ones made by a single company, ACME. [if you are thinking roadrunner and the coyote, you are correct in thinking about the quality of these headliners.]
it was slightly oversize, needing trimmed on all sides, as well as being so stiff, it was very difficult to get into place, even with all the glass out of the car.
it took two of us two days to get that thing in, and another couple of days to very carefully trim the glass openings to accept the rubber gaskets that hold the glass in position, and the rubber gaskets the doors seal against.
it also took several hours to carefully "find" the correct place to punch in the sunvisor retaining holes, as they were not there.
when it was finally done, it looked pretty good, and the owner was very happy with the results, but i told him I WILL NEVER DO ANOTHER ONE !!!!
just my personal life experiences with headliner installations.
your mileage will vary.

Weird - I thought I'd posted an update on this after looking at my RRs.
Guess not, or the question was posted in 2 places.
2/12/67 Lynch Rd car has full headliner, as did my 9/30/67 St Louis car.
2/12/68 St Louis car has the cardboard, which is a familiar memory from a few others I've owned.
Seems to me the cardboard deal was a labor-saving change.
When it happened, I can't pinpoint, but the car, as Zippy says, should tell you what it originally had.

In my original post I stated I have the cardboard pieces - clips and all.

Ten years ago I may have tackled the headliner - not these days - I'm no longer flexible enough and I cramp up quickly. Gonna leave it to the pros !!

So let's say we go ahead with a one-piece install - no cardboards ... on cars with one-piece headliners were there any sort of tack strips along the bottom of the sail panels at the package tray to hole the liner in place ??

Appreciate all the inputs !!

Well a local upholstery guy showed up today and was done and gone in a little over 4 hours. He did a great job for $300. And he also opted not to use the sail panel backers - installing it in one piece as opposed to three.

I'd say you got a deal on that in this day & age.