Bare with me as I am new to this field as well Jack. I think the two objects are too complex for boolean operations. I would separate the geometry of each letter and do difference one by one onto the plate. You can do some quick tests by separating just the first letter, make sure it overlaps with the plate (into the plate slightly) and diff it.
Booleans can be pretty quirky.

You can still parent them if you need to quick select all letters or perhaps it's possible to combine them again once the boolean op's are done.