your set of points are nearly right on, taking them one by one.

1. Under the Laws of War, people are either civilians or combatants.
Agreed - FM27-10 and 1949 GCs.

2. A civilian’s status changes to a combatant once they pick up a gun.
Agreed - same citations

3. The Blackwater folks, under the Laws of War, are combatants for this reason.
Agreed - same citations

4. Under US Law (Goldwater-Nichols), only one person in the region has Combat Command authority and they are (what we use to call) the CINC but now call the Combat Commander.
Agreed - but please note that is combatant command (COCOM). When we reach your next point, we have to deal with operational control (OPCON) and administrative control (ADCON). All of that has no particular legal impact where everyone is military and subject to the UCMJ.

5. It seems to me, that jurisdiction of combatants must fall under the authority of the Combat Commander (no matter who they work for in country).
If we had in-country Unity of Command, your logic would be true. We do not.

Let's take Marines serving as security at a diplomatic mission. All corrections cheerfully accepted, but my understanding is that they normally (1) are not COCOM under the regional combatant commander; (2) are OPCON under the diplomatic chief of mission; and (3) ADCON is retained by USMC. Since they are under the UCMJ, jurisdiction is clear - which is why I like Marine guards.

In the case of Blackwater guards, they cannot be COCOM under the regional combatant commander - they are civilians. I am not familiar enough with their contracts and ROEs, but OPCON and ADCON have to be in DoS and/or Blackwater.

Congress, in facing the contractor issue, ended up going two ways for DoD contractors and their employees: (1) Title 18 (MEJA) jurisdiction in the Federal courts; and (2) UCMJ jurisdiction (as to which, some constitutional questions remain unsettled - and so, perhaps, a bridge too far).

As to contractors and their employees of non-DoD departments and agencies, UCMJ jurisdiction over civilians (even if combatants) seemed about two bridges too far. Congress could have set up an independent court system to try civilians who are combatants; just as it set up the MCA system for the Gitmo detainees (also civilians who are combatants). It did not.

Instead, it extended Title 18 (MEJA) to contractors and their employees "supporting" the DoD - in effect, supporting the regional combatant commander. While Congress could have extended Title 18 (MEJA) to all contractors and their employees, regardless of department and agency hire, it did not do so.

So, Title 18 (MEJA) has a loophole for all non-DoD contractors and their employees who are not supporting the DoD. Since DoD has taken the position that Blackwater security folks are not supporting the DoD, the DoJ has some explaining to do about why the judge should find them "supporting".

I have no problem with your logic - as an argument to Congress that it should amend the statutes. As a legal argument, it will fail in these cases under the current statutory set-up.