Don’t send the parameter values to the root container of the popup, send the string tag path(s) instead. In the popup, use the tagpath with an indirect tag binding on your data entry fields. Make those indirect bindings bidirectional.
This is pretty slick. Any easy way to bind the correct tag is to bind directly to a specific instance of the tag first. Next, switch to indirect tag (the direct path follows) and change the path to the tagPath string that you passed in.