It looks like number 4 is a Keller remake of a vintage style shell. It looks like the poplar wood core is made up of TWO plies -as opposed to the older, original Ludwig 3-plies which had a single thicker piece of poplar. I can tell you that the difference in terms of sound will be unlike that of a true 3-ply vintage Ludwig shell -although I'm sure the Keller is a good shell, too -just not the same as the older original Ludwig shells.
I still can't clearly see the plies in all those examples of pictures, but it LOOKS like, for the most part they are legit and, of those, they appear to be of the mahogany/poplar/mahogany lay-up which I see more of with early 60's drums.
Tell me...When you look at the scarf joint of the shell, itself (not the maple reinforcement ring scarf joint -the shell scarf joint...do you detect any remnant of an old wrap tucked into that area? That is always a good way to detect a true Ludwig shell, too because they used to lay up those old shells by laminating everything flat and then steam bending the whole thing into a cylinder. Where the ends met, they would scarf joint the whole thing -so on all wrapped shells, some of the old wrap was forever embedded into the joint.
Keller shells do not use that process and so, there will be no remnant of the wrap tucked into the scarf joint -In fact, there won't even be a scarf joint on a Keller shell! I think they use off-set laminations instead. The reinforcement ring will be cut differently, too.
Snare buzz, you say? I assume you have checked the wire set for any un-eveness? Never use plastic strips to attach the wire set -use nylon snare cord! Slack off all the way on the tension adjustment and then slowly bring it up to jusssst enough tension that all the strands make even contact with the snare head and don't start cranking the tension up. I would recommend using a 16-strand wire set, myself, but a 20-strand shouldn't be a problem. Make sure the snare wire set is being pulled up evenly. Make sure you have a thin Diplomat snare side head on the drum and not some stupid modern head that is too thick. You need a head that will be thin enough to conform to the snare beds -check that. It could be that someone has re-cut the bearing edges and did not compensat properly for the depth of the snare beds -but Lawton is sup[posed to be good, so I doubt that would be the problem...but I would check it out just to be sure.