I happened upon this patch ...

setting STRIP to (strip-for-target) in #:make-flags (like done for CC) 
would fix this in a simpler way.

Also, that (string-append "DESTDIR=" #$output)) is bogus; it's a bug (*) 
in the Makefiles that it used $(DESTIDIR) instead of $(DESTDIR)$(PREFIX).

install:
	mkdir -p $(DESTDIR)/bin
	cp $(PROGRAM) $(DESTDIR)/bin/$(PROGRAM)

(*) 
https://people.freebsd.org/~rodrigc/doc/data/doc/en_US.ISO8859-1/books/porters-handbook/porting-prefix.html