You could go about this in a few ways. One way to do it without Zero_Qualms' suggestion of ET_GeoWizards and with only an ArcView licence is to create your buffer polygons just as you have done. Then iterate over the buffer polygons, pulling out their geometry and build a new feature class using the geometry but cast it as a polyline instead. See these sections of the documentation to help you (if needed) with reading and writing geometries in ArcPy (scroll down for examples).
The alternative is to write a script to create the line without creating a buffer to copy first. You will need to read the geometries of your lines and progress from point to point, calculating the bearing at each step and then calculating the offset location of your buffer-line. This should be straightforward with a bit of basic vector maths and trig. You can calculate bother the left and right side of the line at the same time. You just need to ensure that the right-side (assuming a clockwise winding) points are added to your polyline so they are in sequential order following the entire set of left-hand points and in the reverse direction. You could do this by having two lists of points and then reverse the order of your right-hand point list before appending it to the lefthand points list to make your line.
Given your updated comment, I will summarize in an answer.
From the online help section "Accessing licenses and extensions in Python":
When using an ArcGIS for Desktop Basic or Standard license, a script
should set the product to Basic or Standard. Likewise, when using an
Engine or EngineGeoDB license, a script should set the product to
Engine or EngineGeoDB. If a license is not explicitly set, the license
will be initialized based on the highest available license level the
first time an ArcPy tool, function, or class is accessed... If the
necessary licenses are not available, a tool fails and returns error
messages. For example, if you install with an ArcGIS for Desktop Basic
license, and you attempt to execute a tool that requires a Standard or
Advanced license, the tool will fail.
Therefore, with arcpy you are not able to "upgrade" or "downgrade" to a different license which is unavailable to the user without getting a failure. Therefore, if you are running ANY single-use licenses on your computer, then that is the ONLY license level you will have available.
For example, if I am a developer running an ArcInfo license, wishing to distribute a tool I developed, I can only test that as an ArcInfo license. I cannot test the tool as if I were running an ArcView license. This of course can be good and bad.
If you forget to (or choose not to) set an explicit license level, and you have a license manager with available ArcView, ArcEditor, & ArcInfo licenses, it will always grab the ArcInfo. In this case, you know all the tools will be available. That's good.
If however, your tool requires edit permissions to an Enterprise Geodatabase, and both your AE & AI licenses are already being consumed by other users, it will grab the AV license, and of course, fail. The same cane be said for GP tools that require higher level licenses. That of course, is bad.
Ultimately, you really only need/want to set your product level if you are using a license manager, and you really want to force the script to use one of the 2 lower license levels.
Best Answer
You could create a new empty table and use cursors to sort your data and insert the rows into the new table (this code has not been tested):