There is another way to get the char confidence number using the XMLExportParams::WriteCharacterRecognitionVariants

This property will write the character recognized as well as their parameters such as charConfidence for each symbol. 

An XML document can be parsed in order to extract the confidence for each character, with this value we can calculate the average confidence for the page. As well as get a detailed description of which characters were not confident enough.

More info on XML export parameters can be found here: XMLExportParams

Note: The downside of this method will be that the export is required instead of result calculation during the recognition, as it was with PlainText.