Hi Angus: Welcome. Take a look at the pics in the JR73 restoration post in this part of the forum, they may provide some guidance on this restitch. I would also recommend you take close up pics of both visors before taking them off the shell so you can see where and how they were stitched on. Look for any markings in the finish of the shell and visor that line up so that you can use these as a guide. For example on the rear visor, the metal spine always leaves marks in the finish of the shell and visor. The KEY to any visor restitch is lining up the holes properly, you MUST make certain that they do or you open up a world of hurt for yourself.
Regarding suitable thread......modern thread has nylon/polyester in it which makes it stronger than the original but it "lights up" under black light. If that does not bother you then try to buy some black upholstering thread or go online and look at the Tandy Leather site which supplies leather crafters. Natural thread...linen can be purchased from book binding suppliers. It will not light up. Cotton which was what was used on all the originals, to my knowledge, is not available today in a suitable thickness for what we need to restitch a helme. If some member has a source then post it here as a response. What I have been able to do....thanks to my mother God rest her soul is source vintage cotton thread from the 1950's. So if that is the route you want to follow, then go on Ebay or the net and do a search.
Last, the Saxon helmet plate you have here does not belong on this helmet, an ordinary brass Prussian line eagle would work as shown in Joe's photo but ideally it should have the proper JR 94 plate, probably impossible to find these days. If you want to see my JR 94 with proper plate, go into the pickelhaube discussion section and look for a post: Dutchy Anyone?