Does anyone have any experience using Briwax for finishing forged items? I've found a few threads on here and around the web about using it, but I just can't get any penetration; the finish just won't stick. I wonder if I'm not getting it hot enough. Any thoughts?

I'm applying it with the workpiece around 350 degrees F. The Briwax bubbles and melts, but even if I apply it heavy and allow it to cool & dry, it buffs right off.

That is how wax works.  You cannot get any significant build up. It is still providing a very thin film of protection.  Wax is soft however, so it is not a particularly durable finish.

There are a number of different waxes found in commercial wax preparations. Briwax is a combination of beeswax (fairly soft) and carnuba (very hard) disolved in toluene. You want to apply it to the workpiece when it's about as hot as a cup of coffee and then buff it smooth. As beammeupscotty notes, you will not get a significant buildup. If you want more of a finish, try "blacksmith's goop", which is equal parts wax, finishing oil, and solvent. The classic version is beeswax, boiled linseed oil, and turpentine, but you can also use other waxes, oils, or solvents depending on personal preference and on what's available locally.

Excellent! My thanks to you both.