Can I make a keyframed item in a mogrt adjustable in Premiere Pro?

I see several problems. The first problem is that you are using a Solid instead of a shape layer for the background so there is no way to adjust the size; you have to use scale. If I wanted to match the Line shape layer to the Solid Width I would use expressions to control where the solid moves based on the width of the background. I would add an expression Control Slider to a Controls null and use that slider to control the width of the rectangle. 

There are no protected regions in your comp, and it is incredibly long for a MOGRT. I would retime everything so that the total comp length was around 5 seconds, and you protect the starting and ending animations. You then have a Graphic in Premiere Pro that has the same transition time on and off the screen, but you can drag to any length you want for the static part of the graphic.

I would also consider making the comp size the same as the frame size of your typical Premiere Pro project. You can add position control for all of the elements and end up with a more efficient workflow in Premiere Pro.

I don't have time to fix your project today, but spending a little time searching "Extended Graphics" with the Search Help field in the top right corner of AE will give you some insights. Every expression that I would create to simplify and streamline the project would be very simple and involve very basic math. Ideally, you want to limit the controls you add to a MOGRT and link as many things as you can to one slider, point control, or checkbox. Most of the MOGRTs I create are designed for 4K video production but have a dropdown menu to reposition the graphic for HD and social media formats, and almost all MOGRTs I create that involve text with background layers have the backgrounds automated by using sourceRectAtTime() to check the size of the text layer and make adjustments automatically. 

I hope this helps a bit. If I get some time I'll post a screenshot that shows now I would link the background and the line graphic together and simplify your rig.