I think that removing the entire board is the only way to do it because you have to scrape off all the old glue to get the new glue to stick. Your local fabric store should have the headliner material in a bunch of different colors, my fabric store even had the 3M glue too. I replaced the headlined on my corolla about a year ago and it looks better than new with no sagging - the car is parked outside too. I followed the instructions on this site:
http://www.wlsheadliners.com/tutorials/toyota-corolla-headliner/