" Consider using construction glue to hold the new molding."

Do you realize how narrow a moulding area you'd actually have to apply
construction adhesive to (I'm talking about the molding face that
actually contacts the wall/ceiling), assuming you were then able to
blindly find studs to nail into in order to adequately the molding in
place until the adhesive dried?

In crown applications on similar vintage homes as the OP, I've
nailed/glued strapping to the ceilings and walls. The nails penetrate
the lathe and hold the strapping in place until the adhesive dries.
Following that, there's always a solid surface to then nail into. Just
be sure not to place the strapping too close to any corner as it would
present problems when it was time to apply the molding.