I contacted Mr. Breen who said this may have been a bug.

They've updated the API and doco at https://www.edrdg.org/wwwjdic/wwwjdicinf.html#backdoor_tag, and the keytype lookupword=n=kana= has been replaced with lookupword|n|kana|.

I can now query example sentences using this URL format: https://www.edrdg.org/cgi-bin/wwwjdic/wwwjdic?1ZEUlookupword|n|kana|

For example: https://www.edrdg.org/cgi-bin/wwwjdic/wwwjdic?1ZEU%E8%BE%9B%E3%81%84|1|%E3%81%8B%E3%82%89%E3%81%84|