Carpet layout, 1950 Champion

I've got my 1950 Champion 4-door sedan in the interior shop right now,
and have a carpet from Phantom, and it's puzzling us a bit.

The front carpet is mostly seamed up around the outside, like it's
supposed to lay in the car without being attached down at the doors,
etc...that seems reasonable enough, especially what with the access
holes and what-not that have to be reached underneath. The rear carpet
is not, however, and so the natural assumption I'd have would be that
the front "arms" of the rear carpet are supposed to run under and be
held down by the door sill plates. But they're not actually long
enough to run up all the way along the door sill plates, and if we do
that they'll stop about 2/3 of the way forward on the door, which seems
a bit odd.

I don't quite recall how these were originally on my car; I have a
vague recollection that there were bits of carpet stuck under the sill
plates when we took the car apart (old carpet was so bad I think we
just cut it out before the sill plates came out), but am not sure.

Is the rear carpet supposed to be attached under the door sill plates?
And is it supposed to stop partway forward on the front door? Any
pointers on this would be very helpful...

Kurt

By way of further note:

If we fasten the front bits of the rear-seat carpet under the
front-door sill plates, then part of the sill plate is being held up by
carpet, while the remaining portion isn't being held up by anything
other than the floor of the car. Is that how this is supposed to be,
or is something supposed to go under the remainder of the sill plate,
or...?