Photoshop can't see colours, and has little to no decision making capabilities. So it can't for example see a colour (or measure a colour), then make a decision on how much to adjust that colour to reach some desired goal.
So, with that in mind, I think what you'd need to do is perhaps something like desaturate the image entirely, make it black and white, then you could apply a hue-saturation adjustment, using the "colorize" option, to achieve your desired colour. This could be recorded as an action, so for example any image you input could be output as a specific colour.
As to automating this using actions and batch processing, there's another problem. You are trying to output different variations of the one image file. Batch processing doesn't work like that. You need to have one image, which is then output as a different file. It's a one-to-one process. If you were to try to use an action to do this repeatedly for each colour, and save each result, the file would just be overwritten for each colour variation. You may be able to address this using a script, but I think it's too complex a task for actions and the batch processor alone.
One possibility, which may or not be practical, would be to duplicate your image file folder 7 times, one for each colour variation. Set up a separate action for each colour variation (7 actions). Then run each action as a batch on each of the folders in turn.