Home made sandblast cabinets..lets see them
Note the old Kitchenaid oven door mounted inside the walk-in door here on my 7 foot oven. Something like that may work out for you too (but it may end up being too small).
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Obviously the glass / laminate in the blast cabinet is going to need to be changed a lot more often than my inspection / temp checker window in my oven does, but I think making a bigger frame for the inside to secure it would be pretty simple and wouldn't demand that you continue to find old oven door windows when it was time for a new one.
What kind of media(s) are you planning on using?