I have nothing to get a precise measurement and I've been to happy hour so don't take this as gospel.
Compared to the 1976 Gibson chrome covers, the German covers appear to be the same thickness. Not identical shapes but very similar. The German made cover fit nicely inside the 76 trim ring, actually with less room for movement than the original Gibson cover (but it doesn't look like it would effect the ability to adjust the pickup as needed). I currently have the original Bach artec pickup (corners trimmed) inside the 76 cover. The German cover fit right over the trimmed pickup with no problem. I tried to upload pictures but Photobucket has some sort of maintanence going on so I couldn't do it. I will try to load the pic's again tomorrow. The Gibsons seem huge compared to the Germans, but it is really just a height difference. The Gibsons look like they are about 1/4" taller than the new covers.