Very nice Dean! 3 ply shells, I would suggest you replace the batter side heads with Aquarian Z-100 coated single ply heads. They typically are a little less expensive than Ambassadors and, according to Mr. Roy Burns, are optimized for the thinner mahogany shells of the 50s-60s, and he insists they will be great on our 3 ply MIJ. I am using them on some of my drums and I love them. They are more responsive and seat better than the Remo heads, meaning you don't have to re-tune after 30 minutes. They are more supple out of the box, the coating is guaranteed not to peel or flake off like the Remo does, and if you do any brush work, the texture of the coating is simply amazing for brushing.
I would start with the batter on your snare just to get a feel for it, unless you can afford to outfit the entire kit all at once. I am certain you will like them better than Ambs, as they are not a "one size fits all head" like the Ambs are (remember, they are purpose-built for thin shells). I fell in love right off the bat when I first played one, but then they were on introductory pricing of less than 10 bucks.
Anyway, feel out your "new" bearing edges. If they are not smooth as silk, take a few minutes and some 220 grit sandpaper. Lightly sand them all the way around, not digging in, just kissing them smooth. This will allow the heads to seat faster and takes away any opportunity for head rattle because of an uneven surface.
EDIT: HERE IS YOUR PEDAL AND MUFFLER ('63 catalog):
http://www.tamadrum.co.jp/anniversary/expansion.php?cat_id=2&now=5