I’m going to once again recommend drillman1 on ebay. I am about 90% sure I have these drill bits at home, so I can throw a piece of cell cast acrylic on my XXL and punch some holes to check if they work.
Here are some 3/32" carbide PCB drill bits that will just clear the 3/8" thickness (they have a 0.400" flute length).
I would also not hesitate to do peck drilling with an end mill either, but that’s just me. If you’re up for that, there are a lot of options as well, just avoid any down cut bits.