You might be able to feel (or not) the braces through the headliner. Did you try and push it at all? Might be able to pop it right out until next time But Id really like to hear more about the dry ice trick.
Kind of depends on if it's the ABS/cardboard headliner or fabric- the hard headliner would make it tough.
One of the "paintless" dent removal services may be able to advise you too.
