I'm not sure what I'm missing here, but
来年の1月には35歳になりますが、サッカーは年齢じゃないということを証明していきたいですし、若い選手に負けないように頑張りたいと思います。(source)
我々はお荷物じゃないことを証明しよう。
Aren't those 名詞節? Is the rule about は not occurring in subordinate clauses lax with 名詞節?
Note on terminology:
I am aware that snail in this answer refers to this type of clause as "gapless relative clauses", but 『日本語文法入門ハンドブック 著者: 加藤重広』, also recommended by snail, calls it 名詞節, which seems to make more sense because it often corresponds with content clauses in other languages.