Are there any tricks of the trade involving shoe polish? I have plenty of that.
Yes, shoe polish is very useful for making your shoes shiny.
I wouldn't bring it anywhere near your strop, though. You don't want a waxy surface - in fact, you want the exact opposite. Neatsfoot oil conditions the leather. I've heard of people using the Williams trick you mentioned earlier (actually any tallow-based soap) for the same purpose. I prefer good ol' hand rubbing, but either of those will work.