A section of ceiling above my front door has been damaged due to a leaky roof, so I need to replace around half of the 7' x 9'-ish entry area. The existing tiles are stapled to furring. However, based on the way the tiles intersect with each other, I can tell they were installed starting at the front door, and then inward into the house. I can't staple new tiles in because the lip where the staple would go needs to be inserted into the existing tile. The tiles in question are Armstrong 12" x 12" ceiling tiles:
My first thought was to install the new tiles the "wrong" way, and use adhesive instead of staples. However, the adhesive I bought (Henry 237 AcoustiGum) specifically says not to use on wood surfaces. After googling a bit, I can't find any mention of someone using adhesive on wood furring. Note that I haven't opened the AcoustiGum, so if another adhesive is required, I'm fine with returning it for something else.
Is there a way for me to avoid replacing the entire room? (One the one hand, I'd like to save myself unnecessary effort, as well as avoid replacing perfectly good tiles. However, I also don't want to do a shoddy job.)
I'm not particularly knowledgeable about home repair, so any input would be appreciated. If I haven't adequately described the problem, please let me know, and I'll try to be more clear.