The results may depend a lot on luck, practice, and trial and error. You might need access to a machine shop to prepare whatever will serve as the "mold".
I wouldn't count on using a process that requires trimming after the glass is cool. The glass can build high internal stress as it cools, and it may have a tendency to shatter if you try to trim it.
To some degree, you can work molten glass at a workbench; press it flat, etc. But your goal is to get it thinner than it wants to be on its own, which means flattening or molding it, and keeping it that way until it cools.
The thinner it is, the faster it loses heat through the surface. You won't be able to put a blob of molten glass on a room temperature metal surface, and press it with another room temperature piece of metal down to 1 or 2 mm thickness. It will lose fluidity or break before it gets there. If you want to press molten glass to your thickness outside the kiln, you would need some high temperature insulating material as the mold. The "practical" approach is to heat the mold along with the glass.
You also need to deal with the air between the frit particles. As the glass melts, the air needs a place to go or it will be trapped in the glass. So you probably can't start with the frit already contained top and bottom. That suggests melting the frit, then flattening it to the desired thickness.
So everything would go into the kiln. When the glass is melted, the top of the mold would be moved and pressed into place.
I can think of a couple of possible methods using this approach:
Create a thin irregular shape, whatever that turns out to be. You might be able to do that with two large, polished metal plates ("large" being something larger than the finished object). The top plate would need to have some weight to it.
Mound the glass frit on the bottom plate, and have spacers of the desired glass thickness in the corners. You might want some external guides to keep the top plate aligned once in place. After the glass melts, move the top plate into place on the glass, and press it down to the spacers. Maybe leave the assembly at full heat for a bit before starting the cool down process. Whatever "organic" shape the glass ends up is the result.
Contain the shape in a polished metal mold with a heavy top plate that fits tightly within the sides when cool (when it's hot, the expansion will leave a gap for air to escape when you insert the top). Play with the amount of material to determine the thickness. The process would be similar to the first case, but the mold would control the shape when the glass is flattened to a uniform thickness by the top.
I suspect you would need this to be somewhat of a hybrid of the two methods. The bottom portion of the mold may need to be a bottom plate with removable sides. This would be not just to get the glass out. A metal mold would contract more than the glass when it cools, which would mean that the mold would become smaller than the material it contains (see where I'm going here?). Unless the mold is a TARDIS (bigger inside than outside), I'm not sure the glass would survive the necessary change in shape to convert cross section to height. The process might require flattening the molten glass inside the mold, then removing the sides of the mold and using some form of spacer to maintain the height of the top. Hopefully, the glass would maintain its shape from the mold.
Perhaps an "easier" way to accomplish this would be to start with the first approach, where you set the height between the top and bottom plates. Once the top is in place on the molten glass, use adjustable sides (which will be a known thickness), to push the molten glass into the desired outline, then remove the sides.
I've never done this, and don't know if, or how well, it would work. But the processes at least deal with the obvious issues, and provide a starting point for experimentation.