I did my last 81 and didn't have any problem. Actually, there are strippers made specifically for this effort. Go to the local auto paint supply store and ask them. Tell them what you've got and they should be able to point you in the right direction. DO NOT go through the gell coat, and bonding strip adhesives! You'll know them because the gell coat will be grey (like primer) and the bonding strips are green, and look like bondo. You don't want to see fiberglass fibers at all! So when people say the "took it down to the fiberglass" that's usually not the case. What they did was strip all the previous paint off. Another thing to watch is anything you use to scrape the paint off when the stripper is used, can and will gouge the glass if you're not careful. Just take your time and you should be able to get those layers of paint off with little problem, it'll just take time. Also, becareful of the nose and tail, you can gouge them too!
Once you get the majority of the paint off, wet sand the rest. I wouldn't use a DA unless your really good with it, it'll only cause you more work later. Then start bringing it back up with primer (a good fiber fill) fogging it, and wet sanding. When it comes to the creases Evo was talking about, come from the fender up and the surround across the crease. If they're not too bad, this will help put them back. If they are gone, you may have to build them up a bit first.
I'm actually looking forward to doing the 81 I have now!!