That "copy" of Apple Personal Diagnostics 1.1.3 is likely an updater for 1.1 or 1.1.1, not a full version. Apple Personal Diagnostics was sold as commercial software, your best bet…
For some reason I was under the impression the LC 2 also could do dual floppies. Anyway in that case I can see a LC 1 being interesting just for dual floppies and you should skip …