First, purchase a copy of Instant On Basic.
The data in the Civil 3D model is data. Styles control how that data appears. So, you can convert a project pretty quickly, but it still takes planning, a systematic approach and a bit of work. Remember to back up BEFORE you start, and test as you go about the process.
emploty Data Shortcuts or Autodesk Vault to share the Feature data you need to move over. Survey Networks, Points, Surfaces, Alignments, Profiles, Pipe Networks all can be moved over this way or by simply referencing the file data into new drawings started from NoStyles Jump templates. You may need to get your existing Points, Point Groups, and Description Keys over via LandXML import and export.
Parcels need to be "moved" with a LandXML export and import and will have to be renamed and renumbered. You should have Sites defined in your existing project for your parcels. Make sure you recreate those sites in the new drawings before you move data over.
Set up your Parcel Feature settings (or any other feature's settings) BEFORE you import or data reference the Civil 3D project data to get the best results. Promote the references to disconnect them from the old drawings. Move and save the old data shortcuts files to another location. Recreate new data shortcuts from the new drawings.
Gradings and Feature lines that are not yet part of or resolved into surfaces are perhaps the trickiest data to move and particularly if the gradings target surfaces. When in doubt you can throw all the Gradings into a surface and/or the Feature lines to a surface as breaklines and then extract them from the shared surface into a new drawing and recreate the Gradings and partial surfaces.
Last but not least are the Assemblies and the manual recreation of the Corridor(s). Assemblies will Copy with Base point from drawing to drawing with the latest service packs installed. Rebulding a complex corridor with multiple baselines and regions isn't hard just tedious.
What about the AutoCAD stuff?
That's easy. Use Map Queries based on Layer Properties with Alter Properties to put them on appropriate layers in the new drawings.
The Jump uses NCS layers and references them in its Styles. The Jump also uses STB templates and NOT CTB templates. You don't want to just drag and drop the Styles from the Jump templates into your CTB drawing files. This makes more work. If you must, it is best to go the other way. Set all the styles for all the existing features and labels to STANDARD in your current drawings. Insert exploded the old drawings into new Jump drawings. Reset the styles to Jump styles. You will end up with some drawing cleanup and purging to do, but it works.