I've used cheap ACE rattle can on engines, several of them, and then followed it up with a quality clear urethane top coat. (automotive) "I" have not had a problem. However recently a member who had been doing that as well, did experience a problem, and he too had done several.
You need the clear coat (quality) especially on a Briggs with a pulsa-jet set up, because the fuel quickly eats the paint.
I've switched over to using an automotive coating exclusively. I use an inexpensive acrylic enamel, but I have also used urethane. These paints hold up to fuel and heat as well, and do not require a top coat.
If you use the VHT, then clear it, you will be good to go, provided the prep work is solid as always.
Lastly, the copper Briggs were sold as industrial engine replacements at hardware stores, which is why the engines used on bikes tended to be the copper ones. The branded machines sold with Briggs were usually spec'd with the other Briggs colors. I cant take credit for that knowledge, as it was discussed here some years ago.
You might drop a PM to Chatten63 or Markus and ask them what they think, as both have extensive experience testing and painting a variety of small air cooled engines.
A word about using a spectrometer on metallic- they don't always accurately pick up the correct hue due to the pearl/flake and give a false paint code. What I did for the bike below was to go to Napa and flip through their NASON chart and find a copper. As I recall, it was from their Fleet chart, and my attempt at making an engine look stock, and old.