You mentioned " I am building a boxed frame on the floor of 2x4s so it stays off the ground a bit" in your first post, that is what I would call a "base", the cabinet will sit on top of it.Not that Melamine doesn't hold screws well in general, but with pocket holes. I have made a table for my mom for the garage with white melamine and the screws are just fine. I used the drill with low clutch speed, so the screw won't be running free in there. But it won't receive the same beating or movement as the large oversized cabinets/doors. My only concern is how to make the base strong and how do I attach the melamine sheets to the base and how should I build a base? Shoot Summ mentioned above the base and the box - I'm not sure what does that means, tbh. I need to see a pic to understand that concept haha.
I'm not really concerned about the exposed screws. But if I want to cover them, I can either use the cover disk, you mentioned, or apply white silicone.
I did not know that melamine had different grades? I did a google search and could not find any "commercial grade" melamine sheets.
I bought these hinges: