I think your best tool, easiest to use power tool option for the job is one of the small oscillating saws. They were originally designed for medical use in safely removing the orthopedic plaster cast without cutting into the patients flesh.
The Fein company designed one for use in woodworking and held a patent on it for many years but it expired a few years a back and now there are many such saws on the market place. Dremel has one called the Multi-Max but companies such as Makita, Dewalt, Ridgid, Ryobi and many more also are selling oscillating saws.
You can rent them if you only need it for a short time.
Don't be afraid to use one, it is not a difficult tool to handle. There will be many videos to watch on youtube including ones produced by companies such as Dremel. I would recommend if you do have to cut through fiberglass cloth that you get one of the blades that has grit on the tip of the saw. But if it is just wood you are going through then one of the blades with saw teeth will work just fine. They also sell blades that can do sanding like functions on the larger flat area of the blades with strong grit material. That will help you smooth off any ragged leftover material so that it does not wear into any insulating materials.
Here is a video from Dremel demonstrating the carbide grit tool in the Multi-Max showing its ability to cut through tough materials. Fiberglass is not nealy as tough as most of what they are cutting through. Dust mask and eye protection are obvious safety needs for any sawing, sanding and grinding task
Too bad you don't live nearby or I could lend you this tool.