Let's not confuse two very dissimilar concepts here. For gas measurement, plate thickness is proscriptively defined by AGA 3 / API 14.3 and may not be deviated from (that is what you would see at Daniels fine web site).
One characteristic that is buried in AGA 3 Part 3 (I think, it has been a while) is a concept of permanent pressure drop. That idea tries to quantify how much of the dP across an orifice plate in gas measurement is transient and how much is permanent. It turns out that the amount that is transient and is recovered is a function of beta ratio and is reasonably easy to quantify. As I recall, low Beta ratios have a very high portion of the dP that is transient and largely recoverable with a thin plate.
On the other hand, the title of this thread is "Critical Flow Restriction Orifice Plates". This is a whole other kettle of cod. For restriction orifice plates you do not want any transient rebound, so the flow path has to be longer (i.e., the plate has to be thicker). I've seen a lot of folks try to quantify exactly how long it needs to be to completely dampen the gross-level transients, but the results conflict a lot. I don't remember Miller talking about restriction orifices (and I'm in Calgary today so I don't have access to my copy of his excellent book), so I can't comment on your vendor's quotation. I know that the book has a section on critical-flow nozzles, but I don't remember it off the top of my head.
Those thicknesses seem kind of short to me, but that is just a gut feel. You don't say how much dP you are expecting. If I were you, I'd make sure that whatever thickness I ended up with would have acceptable bowing with pipeline MAWP upstream and atmospheric pressure downstream with the hole plugged. I ran the 2-inch and got a 0.000035 inch deflection at 600 psid. My criteria for pipelines is 0.1 inch so it would be ok from a deflection viewpoint.
David