Parting is a tough task. I struggled with it for years - applying the suggestions shared above, and gradually worked it out. I guess, like nearly everything else in life, it gets easier with practice. I now find parting off a routine task.
Even still, I don't hesitate to grab a hacksaw, or cut the part off in the band saw and face it clean. It depends on the job at hand.
Are you using a T-blade? My PhaseII part-off blade holder did not have a relief cut for the T of the blade, so the blade leaned over (I cut a relief).
The past couple years, I usually use a carbide insert part off tool - it works great. It is held in a bolt on holder for the PhaseII CXA - drop it in, lock it - no issue.
I have set up a rear tool post (parting tool being upside down - lathe running in the normal direction). This also works very well (chips clear well on deep cuts) - but the conventional works so well that I rarely bother with the rear post.
Let us know how it works out.