Thank you all. That was extremely helpful, and looking at the pictures of Garlattis online, certainly seems to confirm that. This is precisely the kind of information I was looking for. It tells me how I have to proceed with stripping the paint. It appears there's a very good chance the lugs and stays might be plated. I'll approach them very cautiously just in case it can be salvaged.
There are enough of what appear to be the original components that I should be able to put it back together in its original configuration, which is what I hope to do. The only things I really question are the saddle and seat post, and I'm not too anal about those. I don't like what was on the bike (steel post and saddle clamp), although one or two pictures I see suggest that might have been original.
The original wheels had the high-flange hubs, with steel rims and galvanized spokes. I've already rebuilt the wheels with aluminum rims and stainless steel spokes, ao clearly I'm not going for pure authenticity, but the original rims were pretty rusty, and the galvanized spokes looked really bad.
I'll post more photos of the frame as I continue with the paint removal, especially if I discover anything interesting.