Note the call to make-inspector in the structure definition. We need an inspector to "see inside" the structure otherwise print-convert can't see the contents of the structure.
Note that print-convert is in general useful for serialization purposes.
Please remember that when further converting a print-converted list into a string with, say, format, you need to use "~s" instead of "~a" in the format string (so that the value is output with write instead of display).