This would be something along the lines of the Head-to-Head forum.
To take part in the Courtroom Forum the participants would need to outline their case prior to starting the thread just as they currently need to do for Head-to-Head.
The idea in its Simplest Form:
Here's the basic idea in brief.
Like Head-to-Head the two debate participants state their initial cases in a request to start a Courtroom Thread.
Unlike Head-to-Head they must also request a "Judge" to oversee their case.
The Judge can be anyone:
Someone the participants chose themselves and agree upon.
Or perhaps they just welcome anyone to volunteer to be their judge
Or, because the Forum Exists (assuming it is created) there could be a thread where people who would like to be a judge post their name on a list of "Available Judges".
Then the participants can have a list of judges from which to choose.
Again, in its simplest form, there would be three participants.
1. The Judge
2. Debater #1
3. Debater #2
The Judge would open the thread and ask each debater to present their initial cases. The Judge would then be in charge of deciding which points the Judge would like the debaters to elaborate on specifically.
The Judge would be in full control of the debate going back and forth between the debaters until the Judge decides he or she has enough evidence to make a final ruling. The Judge then pronounces the ruling and that ends the case.
This could be an interesting forum I think: People could always ask for a retrial and a different judge. And no one will ever be incarcerated.

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More Elaborate Ideas:
I certainly don't want to bog down this original idea with unnecessary baggage.
But if a simple Courtroom Forum works out, it could potentially grow to become a bit more elaborate.
For example within the thread there could be the three active posters as I've mentioned above:
1. The Judge
2. Debater #1
3. Debater #2
However, there could also be an additional "jury" that has been selected to simply read the thread. The Judge could then ask the jury for a "verdict" and simply pronounce the verdict that the jury has rendered. The jury could be any size, but should also be selected before the court thread starts.
Also, it could be possible to call "*Expert witnesses" These would be people who would be called into the thread at the request of the debaters and approval of the judge and permitted to post. The two debaters could then question these *expert witnesses* just as in an actual courtroom.
*the only expertise an expert witness is required to have is the fact that a one of the official debaters called them in as such. And of course they would need to agree to be a witness.
The witnesses would then be excused, everything being controlled be "The Judge".
I think it could be great.