Based on the various comments, parting seems to be more of an art than a science, It seems that those who have claimed to have mastered the art have tried the different method s and their professed method is the very best way. Curiously, they don't seem to converge on any one method and some, like the one above, are radically different.
There are a few things that seem to favor successful parting. One is rigidity and another is power.
A rigid setup is less likely to chatter, chatter being an alternating gouging and backing out of the parting tool. This includes a rigid setup for the part, as close to the chuck as practical, a rigid tool setup. heavy tool post, and a rigid frame (= big lathe).
Power is self explanatory. Heavier cuts seem to work better than light cuts and they are favored by a lot of torque.
Unfortunately, hobby class lathes don't offer either. Also, it unfortunately seems that all the videos teaching us how to part are runnin big honkin' machines.
As to why it should work better to invert the parting tool, the theory is that if it catches, it will be pulled down and out of the work. That should prevent stalling type grabs. However, it is essentially the same condition as chatter. It does throw the swarf down though and lessen the likelihood of jamming the parting tool.
As to cutting from the reverse side, to the part, the tool looks the same in either configuration. There are some geometry differences regarding the carriage, the cross slide and the compound which might play a part in the efficacy though. I would expect that it varies quite a bit from lathe to lathe which might explain why it works well for some and not others.
Good lubrication seems to be somewhat universal but I have seen videos of parting steel without lubrication that looked like they were parting butter. I have notice in parting that there often seems to be a sweet spot in the cut where it is cutting flawlessly. Inward of that diameter it goes south again. Unless you have a variable speed and power cross feed, there isn't much you can do about this though.
Super sharp cutting tools with good geometry are also essential as are proper tool setup. Out of the box, the parting tools come with zero rake. If you come in on center, that is what the part sees. If the tool is raised slightly, the part sees a tool with positive rake. Clearance has to be enough that the bottom of the tool doesn't rub though. Again, the lathe geometry and rigidity come into play here.
Bottom line, don't be afraid to try the various methods. Find the one that works the best for you. I'm still looking for the best one for me.