Congress CAN "interfere" with military justice. In case you haven't noticed, Congress makes ALL the rules. It's in Section I, of the US Constitution.
Since it is codified as Title 50, Chapter 22 of the United States Code, the UCMJ goes through the same process as any other legislation.
To "change the rules," Congress must (a) pass legislation through both the House of Representatives and the Senate, and (b) either obtain Presidential approval of the change, or override the President's veto.
In case you didn't notice...Congress didn't do any of this.