MOGRTS: properties not translating when exporting from WE to Premier

I've downloaded the AEP file, and exported a .mogrt file. Not sure why your animation is not coming through, but there are so many unecessary layers and excessive parenting going on that it's hard to wrap my brain around what's going on. I mean, it's a simple MOGRT with basically four layers. 2 shapes and 2 text layers. Why 10 layers? You need only one extra Controls layer to make this work - as explained in the PDF that Neil linked to.
And why would you want to have the user make all of these adjustments manually? You should build the MOGRT to be easy to use. Having to drag a lot of sliders to adjust the layout is NOT user friendly. You need to make those bars adjust to the size of the text layers, and be responsive (as explained in the PDF).

I suggest that you re-build this project from scratch, and use sourceRectAtTime() expressions to make things adjust automatically, instead of adding a bunch of unnecessary adjustments and layers. Plus, the shapes Position should be animated directly, not via Null Objects. Also, look into Responsive Design - Time to make the length adjustable in Premiere Pro without affecting the animations.

There's no bug in the 23.6 version that would cause this that I'm aware of. 

Have you checked through the free ebook Adobe makes available, Making Mogrts, by noted expert Jarle Leirpoll? He demonstrates the process of making from simple through fairly complex mogrts in a very clear process. From planning through building through the important step of deploying to a team.

Jarle’s Making Mogrt’s ebook on Adobe blog