In your "Extraction phase" you can use the strip-components flag like
tar xvf tarname.tar --strip-components=n
which will remove the first n leading components of the file name. Although if you have different file-path-components this will not work for all cases.
If you want to do it while archiving, only one thing comes to mind, and I will share
INPUT: list of files + full paths
1) for each line, split the path out of the filename
2) execute cd to that path and tar on that filename
3) repeat for each line
