McMaster Carr sells a lots of different solid rivets.
http://www.mcmaster.com/

If McMaster does not have the size you need then http://www.bigflatsrivet.com/ often does, but they cost more.

I see no reason why you should not re rivet them as they were originally. I have replaced many solid steel rivets in different cars, including 3/8" frame rivets in my 2 ton. with some simple home made tools and a torch you can do it yourself. Try searching for "rivets", as I think I have explained how to install "hot rivets" before on this site. The smaller ones can be worked cold in the same way.

Grigg

•1951 GMC 250 in the Project Journals
•1948 Chevrolet 6400 - Detroit Diesel 4-53T - Roadranger 10 speed overdrive - 4 wheel disc brakes
•1952 Chevrolet 3800 pickup
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"First, get a clear notion of what you desire to accomplish, and then in all probability you will succeed in doing it..." -Henry Maudslay-