Yah, I would be careful as well. But, of all the photos I have seen posted on here, I don't remember any showing were one or more of the doors were busted. Sometimes they had fallen out, but were still there and not broken. They may be made of that tempered glass like correl dinner ware. It is strong stuff, but if it does break, look out.
Thanks Jon - Real confidence builder.
! I know you will do fine with it, Joe.
!
I should have put aWell, it IS strong or it wouldn't have survived all these years. And, at least if something bad happened "diamonds" are better than long sharp slivers
I wish you weren't so far from our Upper Midwest TVWBB Meet. We would love to have you there. Maybe you need to do a road trip! There should be some good bargains on parts to buy or swap for
at the end of the last post. They are safely sitting on a table in my basement all cleaned, and hardware reinstalled, after a long soak in vinegar to remove the rust from the hinges. 
You don't think I should use the original boards? I haven't started on them yet, but I think they look like they may be in ok shape. I wonder what kind of wood it is as it is very light weight. The wood handle for the grill is warped if you look at the picture. I have seen a picture of a solid piece of wood being used and think it looks nice and more modern. But I do have the original in a vice right now trying to get it to straiten out. I am a little torn between "improve" it or as "stock" as possible.
Might think about a 9057 “Grill out light” for handle replacement? Sure you can use the originals, take one in to the hardware place and have them color match it. If it were me, I’d make it stunning. I’m biased, I’m lucky enough to have a cabinetmaker buddy that seems to have an unimaginable inventory of nice material. I think I might be tempted to do one in mahogany sometime.
Soak the handle in water for a day before you try to straighten it. Then leave it in the vice until it dries out.