Hi silly-grocery,

The painting in Forger is based on Vertex paint. It doesn't use any texture file internally for this.
The texture export is then file-based, and after checking with the Forger team (hence the delay based on the weekend), this is not changeable inside the application.

However, if you save it as a Cinema 4D file, the Vertex Colors are stored in a Vertex Tag. This means that all the data you have provided in Forger is available.
The texture can be baked to a higher resolution depending on the Mesh density.

All the best