Bumping dead thread to add info for anyone in the future looking for more info - After calling multiple local glass shops and being denied, I was referred to these guys based in Washington State
https://www.onedayglass.com/order-online/
After speaking to them and discussing this project, I learned there are two types of tinted glass, light grey and dark grey. Dark grey is used for car window tint, it is too dark for arcade monitor glass. Light grey is the most likely tint for this. (Other ways of tinting involve putting a decal on top of glass)
Laminate / Safety glass is what I ordered. As far as I could tell, this is what you want if you are going for the stock look.
Here's my order. I couldn't get the flat, 1-step bevel on all edges for some reason, probably due to the type of glass, so I asked them to pencil-grind the edges instead. I selected the matte/satin option.
Laminate / Safety Glass
Shape: Rounded Corner(s) (a, b, c, d)
Thickness: 1/4"
Tint: Light Gray
Edgework: Pencil Grind All Edges
Hole Size: 3/8"
Hole Quantity: 4
Total order including shipping was $260 USD. If anything doesn't fit, looks weird, or the weight is off or whatever, I'll update the thread and try again.