The vacuum pump is a booster pump. The engine pulls vacuum as well. So those two lines you see in the diagram (one to the intake manifold and the other to the pump) are both pulling vacuum to assist the brake (third line).
When the pump goes bad, it should pull less vacuum, not more. So I don’t see how a bad pump would pull more oil into your intake. I know that’s what the one poster commented in that video, I just don’t understand the mechanism by which that was happening.
To be sure, oil can get into your intake from the PCV breather. In fact, I can tell you for certain that the newer cars have a bit of an issue (in my opinion) with how much oil gets past that breather. Most people that have pulled the superchargers have noted the accumulation of oil. The vacuum generated by the engine at the intake manifold might pull some of this down into the cylinders. However, the vacuum is greatest at idle and the throttle plate is closed. It is far less when you accelerate (especially hard acceleration), and even on first startup when the engine is idling fast because the throttle plate is open and air is flowing in freely from the air intakes.
You mentioned that the PCV was changed. I assume this was after the smoke started. How bad was the PCV - was it torn? Just wondering if you got a bunch of oil in the intake while the PCV was torn, and its still draining into the cylinders. Seems like it should be out by now though.
You could try disconnecting the purge valve as mentioned before - just rule out the evap system.
If your thinking of disconnecting the brake pump, be careful as that can be a bit dangerous. Your brakes will not work nearly as well without that pump connected. Might be okay to observe the startup smoke.
Not sure if you’re doing this work yourself or not, but you might just pull the intake manifold and see what’s in there. I don’t think it’s very much of a job on the V8’s (it’s a royal pain in the supercharged cars). With that off, you could see if there’s oil accumulating from the PCV, and you could get a peek at your valves/stems to see if there’s a lot of carbon buildup or even fresh wet oil getting past. Just make sure not to let anything drop down in those cylinders

.