OK - so the drive doesn't appear to be the issue. Next thing, can you
actually play the discs without them stuttering ? Also have you tried
the direct copy/paste procedure and does that take ages or is it much
faster ?

Presumably the system works well otherwise ?

Since you appear to have a spare drive at least temporarily, try
booting up with a Live CD with the second drive in place then try to
copy audio from a CD in the other drive. This will check for errors in
Ubuntu itself and if just as slow you are looking at a hardware error
somewhere.